We study Parseval frame wavelets in L 2 ( R d ) with matrix dilations of the form ( D f ) ( x ) = 2 f ( A x ) , where A is an arbitrary expanding n × n matrix with integer coefficients, such that | det A | = 2 . In our study we use generalized multiresolution analyses (GMRA) ( V j ) in L 2 ( R d ) with dilations D. We describe, in terms of the underlying multiresolution structure, all GMRA Parseval frame wavelets and, a posteriori, all semi-orthogonal Parseval frame wavelets in L 2 ( R d ) . As an application, we include an explicit construction of an orthonormal wavelet on the real line whose dimension function is essentially unbounded.