In this paper z-transform theory is used to develop the discrete orthonormal wavelet transform for multidimensional signals. The tone is tutorial and expository. Some rudimentary knowledge of z-transforms and vector spaces is assumed. The wavelet transform of a signal consists of a sequence of inner products of a signal computed against the elements of a complete orthonormal set of basis vectors. the signal is recovered as a weighted sum of a basis vectors. This paper addresses the necessary and sufficient conditions that such a basis must respect. An algorithm for the design of a proper basis is derived from the orthonormally and perfect reconstruction conditions. In the interest of simplicity, the cases of two and higher-dimensional signals are treated separately. The exposition lays bare the structure of hardware or software implementations.