Maurice Sendak (1928-2012) cultivated an image as a curmudgeon. "I'm not Hans Christian Andersen," he told Bill Moyers. "No one's going to make a statue in the park with a lot of scrambling kids climbing up me. I won't have it."

Sendak had a particularly good, cranky run in the last year of his life. He appeared on "The Colbert Report," ripping the current crop of children's books as "abysmal." He was interviewed by Emma Brockes in The Believer magazine, and he declared about e-books: "I hate them. It's like making believe there's another kind of sex. There isn't another kind of sex."

He was a hot mensch.

Anyone who's spent time with Sendak's best books - "Where the Wild Things Are," "In the Night Kitchen" and "Nutshell Library" among them - knows that this querulousness was the salt crust on a deep and complicated well of feeling. He was also the man who said: "I cry a lot because I miss people. They die, and I can't stop them. They leave me, and I love them more."

Sendak's posthumous new book, the last completed volume we are likely to get from him, is "My Brother's Book," written in memory of his brother, Jack, who died in 1995. This lovely if evanescent book - it deals with the great Sendakian themes of loss, danger and flight - also feels on an unspoken level like an elegy for his companion of a half-century, Eugene Glynn, who died in 2007. The line that hangs over it is this one: "A sad riddle is best for me."

At the beginning of "My Brother's Book" a great screaming comes across the sky. A new star slams into Earth, separating two brothers, Guy and Jack, and heaving them out of paradise. Jack is catapulted "to continents of ice." He is "a snow image stuck fast in water like stone./His poor nose froze."

Guy, on the other hand, goes tumbling down into "soft Bohemia" and into the lair of a polar bear who threatens to eat him "bite by bite." Guy ultimately does allow the bear to devour him. In death he goes "sweeping past paradise" to rejoin his brother.

"My Brother's Book" has echoes of Shakespeare's "Winter's Tale," the play that contains the stage direction "Exit, pursued by a bear," and it contains some of Sendak's richest and most incantatory language. When Guy poses a sad riddle the bear cannot answer, we read:

"To hell with you then!" the bear uproared,

Shadowing the sky, bellowing up a whirlwind

And slanting wide the world to the winter side -

And with his mighty paws scattering himself

Into a diadem of noble stars

Befitting Ursa Major.

In his foreword to "My Brother's Book," the Shakespeare scholar Stephen Greenblatt notes how Sendak seems to have picked up on Shakespeare's evocation, in "The Winter's Tale," of "unpathed waters, undreamed shores."

I was put more in mind of a line from "Mansfield Park," in which one of Jane Austen's characters declares, "What strange creatures brothers are!"