To gain physical interpretations and insights from observed phenomena, it is often desirable to decompose a given function, i.e., the observed signal, into a set of nonorthogonal functions. This paper describes a signal processing algorithm based on the minimization of the mean-square error formulation of the decomposition analysis. The computation scheme is derived from a recursive gradient descent method to approach the correct answer for a set of over-determined simultaneous equations. The traditional matrix inversion technique is usually not workable for numerical operation because the matrices are often ill-conditioned. This suggested approach not only alleviates the computation problem, but also can more easily be implemented in a parallel architecture computer or a neural-like network. The signal received from a synthetic circular array [N. Yen, IEEE/JOE, Jan. 1992, pp. 40–47] is used, as a practical example, to illustrate that a composite signal can be reduced to a combination of the corresponding signals from various directions. Comparison of the results obtained by this algorithm with the traditional beamforming method supports the use of this new signal processing technique.