LetP=NAMbe the minimal parabolic subgroup ofSU(n+1,1), which can be regarded as the affine automorphism group of the Siegel upper half-planeU n+1 ,Palso acts on the Heisenberg groupH n , the boundary ofU n+1 . ThereforePhas a natural representationUonL 2 (H n ). We decomposeL 2 (H n ) into the direct sum of the irreducible invariant closed subspaces underU. The restrictions ofUon these subspaces are square-integrable. We give the characterization of the admissible condition in terms of the Fourier transform and define the wavelet transform with respect to admissible wavelets. The wavelet transform gives isometric operators from the irreducible invariant closed subspaces ofL 2 (H n ) toL 2 (P).