The aim of the paper is to present an orthogonal basis for the discrete wavelets in the general structure of the spline-wavelet decomposition. Decomposition of an original numerical flow without embedding in the standard functional spaces is discussed. It makes it possible to concentrate on simplification of the realization formulas: here, the simple formulas of decomposition and reconstruction are presented, an orthogonal wavelet basis is constructed, and an illustrative example is given. Finally, some estimates of the complexity of the method discussed for different software environments are provided.