Wavelets are useful for many applications including signal and image processing. Tensor product has been a predominant method for constructing multivariate wavelets. In this talk, I will briefly review the limitations and benefits of the tensor product construction. Then I will introduce a new alternative to the tensor product, to which we refer as coset sum. We will see that many benefits of the tensor product are shared by coset sum, while some of its limitations are overcome by coset sum. Highlights of the coset sum approach include the following: the coset sum works for any spatial dimension and for a wide range of lowpass filters, and it can be associated with wavelets that have algorithms faster than the tensor product ones. Some experimental results that compare the performance of the two methods will be presented.