A new mathematical derivation is developed for the solution of the problem of nonlinear inverse filtering. It is derived for systems with finite deterministic signals, i. e., the output y of the system is a finite set of data samples. It is assumed that the system generating this output can be represented by a discrete Volterra series, the kernels of this series being known. With knowledge of both the output and these nonlinear kernels# the model is derived for the nonlinear inverse filter. The output of this filter x<n) is the best approximation to the original input x(n) in a least squares sense. In order to guarantee that the series will converge, it was assumed that the nonlinearities are not too violent. Under this assumption, the proposed formulation works well. It has been tested with quadratic and/or cubic nonlinearities in the system. In these tests, the inputs used were a sampled unit step and a sampled sinusoid.