A theorem is proved that provides a finite algorithm to represent any BOOLEan function f as a BOOLEan expression whose argumen are at most three BOOLEan function of the variable appearing in f. The interation of the algorithm will generate, in a finite number of steps, and expression of the original function as a BOOLEan polynomical whose arguments are linearly separable functions of the original variale each of which may, furthermore, be required to satisfy additional optimally conditions.