The authors introduce a very efficient algorithm, based on real-time optimal-order spline interpolation for computing the integral wavelet transform on a dense subset of the time-scale domain with a compactly supported spline-wavelet as the analyzing wavelet. We remark that in this work the semi-orthogonality property of the spline-wavelet is essential, and the computational complexity of their fast integral wavelet transform (FIWT) algorithm does not increase with the increasing number of values of the scale parameter. In the last section they present a few examples to elucidate the applications of their FIWT algorithm.