The　concept　of　monotonic　value　is　presented　to　predetermine　the　optimal　or　near　optimal　number　of　hidden　neurons　needed　in　a　feedforward　neural　network　with　one　hidden　layer.　The　approximation　of　an　estimated　neural　network　to　y=sin(2pix)　is　well　simulated　and　the　monotonic　value　of　Xor　is　proven　to　be　2.