In this paper a method of test and realization of non-linearly separable switching functions that are 2-rcalizable, i.e. realizable by a network of 2-threshold logic elements is presented. The positive linear dependences among the rows of the coefficient matrix of the set of inequalities representing the function are first determined and systematically removed using a distribution table. All possible solutions are readily obtained. A weight matrix representation of a network of threshold logic elements is used. An example is worked out.