The most promising approaches for optical neural networks are based on intensity encoding. However, a serious drawback of intensity encoding is the lack of negative values and optical subtraction, which are essential for rendering neural networks useful. To overcome the need for optical subtraction a novel training method is described here that is especially useful for optical multilayer neural networks. In this method, subtraction is implemented as a transformation of the interconnection weights which makes possible the implementation of multilayer perceptrons with optical thresholding. The method is straightforward to implement in optical neural networks where learning occurs under external electronic/computer control.