BOOK REVIEW / Peekaboo quiffs and eel-spears: The Annals of Chile - Paul Muldoon: Faber, pounds 14.99: Jamie McKendrick unravels the dizzying delights of Paul Muldoon's new poetry collection

WHEN Baudelaire claimed that a poet's head should be a dictionary of rhymes, he hadn't dreamt of anything as intricate as Paul Muldoon. In his last book Madoc - aptly subtitled A Mystery - Muldoon employed consonantal rhymes with a dizzying sophistication and variety. The enigmatic prose-poem which prefaced that book ('The Key') ends with his 'footfalls already pre-empted by their echoes', an image which perfectly describes the subtle disturbance of his way of rhyming.

In his new book, 'Yarrow', a long piece composed of 150 short poems, takes rhyming into new territory. Muldoon operates a kind of telescopic or long-distance rhyming whereby a poem rhymes not with itself but with another poem, usually adjacent to it. Where Muldoon speaks of the yarrow, mock-pedantic plant-book description soon shelves into a teasing evocation of his own procedure, the way his rhymes have been placed just beyond the threshold of audibility:

'With its bedraggled, feathery leaf

and pink (less red

than mauve) or off-white flower,

its tight little knot

of a head,

it's like something keeping a secret

from itself . . .'

The complexity of the scheme is mirrored by the poem's allusiveness - from Camoes to Hart Crane, Ovid to O'Rahilly. This can be more playful than purposeful, and the fabric of references to adventure stories, chivalric romances and television westerns seems to have become an end in itself, hindering the poem's movement. Among the poem's fund of languages - Latin, Spanish, neologisms, place-names, etymologies - Gaelic shares the line with English more insistently than ever before in Muldoon's work.

The best poems, though, are all in the first part of the book. The long 'Incantata' for the death of the Irish artist Mary Farl Powers puts Muldoon's complexity to its most moving use. This extraordinary poem is impelled by a desire to name and include everything that has been lost with the loss of the person and achieves an uncanny restitution. It's an elegy unlike any other - intimate, humorous and heartbreaking.

A poem for the birth of his daughter reveals a similar delight in language and in 'the inestimable / realm of apple-blossoms and chanterelles and damson and eel-spears / and foxes and the general hubbub / of inkies and jennets and Kickapoos with their lemniscs / or peekaboo-quiffs of Russian sable' into which 'Dorothy Aoife Korelitz Muldoon' is hauled by way of a Caesarian.

Muldoon has always considered the world through an Ovidian prism, so that something is no sooner one thing than it's become another. Here, his translation of Ovid, though the rhyming in couplets is more conventional than might be expected, is superbly skilful, as is his version of Vallejo, which catches a tragi-comic tone no other translator has detected let alone caught.

In 'Monarch and Milkweed', another poem from the first part, Muldoon perhaps has in mind Frost's poem 'Pod of the Milkweed' where droves of butterflies are drawn to this 'drab weed'. If for Frost 'waste was of the essence of the scheme', there is nothing wasteful about Muldoon's poem, or his rhyme-scheme - essentially that of the extended villanelle, with one rhyme anagramatically transposed onto the other: 'He'd mistaken his mother's name, 'Regan', for 'Anger': / as he knelt by the grave of his mother and father / he could barely tell one from the other.' The conflation of name with emotion, of one grave with the other, and of the milkweed with the monarch butterfly is brought into being as much by the twin rhymes as by the play of his images.

It's this mixture of chance and fixity, or ordered chaos, that makes Muldoon's rhyming so exceptional. His rhyme-words seek each other out in the most unexpected places, finding a phonetic pairing which is the equivalent of the biological link between the butterfly and the milkweed: 'Then: 'Milkweed and monarch 'invented' each other'. That Muldoon should see the graves of his parents as an occasion to meditate also on the nature of language and sound may strike some readers as curious. But his formalism is so thoroughgoing that rhyme becomes a principle governing the secret, powerful affinities between things and between people.