As Helen Macdonald notes, animal books rarely end happily: Henry Williamson's Tarka is killed by hounds, and the otter in Gavin Maxwell's Ring of Bright Water is beaten to death by a man with a mallet; the deer in Marjorie Kinnan Rawlings's The Yearling is shot. Richard Adams's Watership Down is, in its sappy, mystical way, a little more hopeful. Hazel survives. All the same, the reader must come to terms with the loss of Woundwort, who is savaged by dogs, his body never found.

Macdonald's H Is for Hawk turns all this on its head, beginning as it does with a death – and a human one at that – and ending with a flare of optimism as her goshawk, Mabel, is safely installed in the aviary where she will spend the moulting season. For Macdonald, this is a painful parting. Their peculiar intimacy is temporarily at an end; the next time they meet, they will be strangers again. But the reader knows by this point that Macdonald will be able to bear the weeks ahead, that she is restored to herself and to those who care about her.

Mabel's cold gaze at the aviary's cinderblock walls might well induce her to flinch inwardly – I'll miss you, she thinks, even if you won't miss me – but there is calm and quiet buoyancy in her prediction that the bird's ochre feathers will soon be "barred stone-grey and white". She is able to accommodate change – perhaps even to find succour in it – and we may breathe a sigh of relief.

H Is for Hawk, as you will perhaps have worked out by now, tells the story of how one woman deals with grief by training a goshawk. This isn't as strange as it sounds: Macdonald, who became obsessed with birds of prey as a child, has flown many falcons over the years, and it's her father who has died so suddenly, a man she associates strongly with her passion (a press photographer, he and his daughter were good companions, sharing a certain beadiness and the ability to be vastly patient). But in another way it's perverse. Goshawks are by reputation the ruffians of falconry, being bloodthirsty, temperamental and supposedly difficult to tame. "The names usually bestowed on her are a sufficient index to her character," writes Captain Gilbert Blaine, one of the authorities Macdonald loves to quote (he was writing in 1936). "Such names as 'Vampire', 'Jezebel', 'Swastika' or even 'Mrs Glasse' aptly fit her, but would ill become a peregrine."

Why, then, is she so determined to have one? Partly, it's that the gap left by her father is so unfathomably huge. She needs something big, literally and metaphorically, to distract her, to stop the awful ticker tape of loss that runs through her brain. Partly, it's that she has a thing for TH White who, long before he published The Sword in the Stone, wrote a memoir called The Goshawk, in which he gave his own account of training such a bird (it was eventually published in 1951). In the past, White's monstrous and often cruel battles with his hawk, Gos, repelled as much as fascinated Macdonald (amazingly, she read this book at the age of just eight). In mourning, though, she feels a tender new kinship with him. His loneliness and isolation: isn't this her plight too? The reclusion of grief makes misanthropes of us all.

Macdonald tells the story of White, a sadist who fantasised about spanking schoolboys, in tandem with that of her taming of Mabel, and it's never anything less than interesting, her attentive sympathy for this repressed and unlovable schoolteacher stirring the reader to feel something similar. Impossible not to ache as you read of his loveless, brutal childhood (it's a catalogue of misery, but I was most horrified by the letter his mother wrote to him at boarding school in which she urged her boy to hold in his lips, if necessary with his teeth, because they were "growing sensual").

But it's Mabel who keeps the book in your hand. Bought for £800 cash on a Scottish quayside, she emerges from the box in which she has been transported like "a griffin from the pages of an illuminated bestiary". Macdonald cannot at first get over how reptilian she is, "the lucency of her pale, round eyes… the waxy, yellow skin about her Bakelite-black beak… half the time she seems as alien as a snake, a thing hammered of metal and scales and glass".

However, she does have bird qualities too, and it's these that make her lovable. She likes to play with a ball of crumpled paper. The sulkiness of the goshawk. Is it a myth? Macdonald thinks it might be. Go back to the 17th century, before falcons became all the rage, and the authorities claim for goshawks other qualities: sociability, familiarity, even fondness.

I can't remember the last time a book made me feel so many different things in such quick succession. It's difficult to be with grief. It's exhausting; your life-grabbing instinct is to get away from it, which is what makes it so lonely for those in its grasp. There were times when I felt like I could not bear another moment of Macdonald's sadness. It's fair to say that she goes a little mad. But then she would head out with Mabel on her arm, and it was as though the clouds had cleared, every sentence a blessing, like the sunshine of early spring.

Her descriptive writing, startling and devilishly precise whether she is in woodland "washed pewter with frost" or chalky fields with a "furry tint" of tiny tillers, is only the half of it. She has written her taming of Mabel like a thriller, slowly and carefully cranking the tension so that your stomach and heart leap queasily towards each other. Always, you're waiting for the moment when Mabel at last flies free. Will she return safely to Macdonald's fist? Or is her owner doomed to spend a long night beneath a tree, listening desperately for the sound of her bells?

And once this landmark is passed – it takes a while, requiring great skill, guts and a working knowledge of the most wonderfully arcane vocabulary – there's the hunting. I won't pretend I was horrified by this. I loved it. It was all so incredibly exciting. When Mabel uses her speed and her talons to kill her first pheasant, she realises for the first time what she is for, and when Macdonald sees this – she plucks the bird with her, "unconsciously as a mother helping a child with her dinner" – and puts it on the page, everything seems somehow to fall into place. People like to talk of the "natural order". They use the phrase to make all kinds of specious arguments. But for me, here it was at last. Suddenly I could see so clearly, it was as if Macdonald had passed me her binoculars. A sated bird. A grieving woman. Loss. Reward. Remembering. Forgetting. Life has a pattern, it goes on, and though relentless, this is also a balm.