By making a discrete finite time signal periodic, it is shown that nonorthogonal B-spline wavelets can be used in a discrete wavelet transform with exact decomposition and reconstruction. A non-recursive algorithm using only Finite Impulse Response filters (FIR) with complexity O(N^2) is presented. The complexity is reduced to O(N log(N)) by using Fast Fourier Transforms (FFT). A faster algorithm is obtained by using recursive filters in the decomposition or reconstruction of the signal. The recursive algorithm has complexity O(N), and the same accuracy as the others. By allowing non-symmetric wavelets, an exact orthogonal reconstruction algorithm is shown, which also has complexity O(N).