The Wavelet Transform (WT) employs nonsinusoidal bases of compact support. The basis sets gab(t) equals g((t-b)/a)(root)a are called daughter wavelets, which are constructed from a mother wavelet g(t) by means of the dilation operation with parameters a and the translation operation with parameter b. Normally, the mother wavelet g(t) is required to be an even function with (integral) 0INFdfG(f)2/f<(infinity) , to guarantee that the basis set is complete. We show that the mother wavelet can be causal instead of even and still guarantee completeness. This allows mother wavelets to be selected that better match causal input signals. A parallel optical WT architecture is sketched.