In this note the successive-higher-ordering method for testing and realization of threshold functions is applied to the realization of a threshold function F, such that it will contain a given function F1, which may or may not be a threshold function, and such that it will be contained in F1+FÂ¿, where FÂ¿ is the function representing the don't care vertices. Before the application of the successive-higher-ordering method, the given functions F1 and FÂ¿ = (F1+FÂ¿) are first changed into unate functions by the successive positivizing of the functions with respect to the variables, one at a time. Some theorems relating to this formation of unate functions are presented. A systematic procedure for testing and realization is developed. An example is given for illustration.