It has been shown that synthetic phase-only filter formed by using different plane wave carriers may provide very high optical efficiency and can produce very sharp correlation peaks in the case of multiobjects correlation recognition. Binarizing the synthetic phase-only filter (SPOF) would make filter making much more easy. But binary synthetic phase-only filter (BSPOF) would produce undesirable noise which mainly consists of convolution-like peaks in the output plane. These noise peaks may sometime rise very high especially when objects are symmetrical. In this paper a random phase mask placed close to the BSPOF in the Fourier plane is used in the correlation system. It can spread the energy of the noise peaks in the output plane. So that, there is no any obvious noise peaks presented, however, at the same time, the sharp correlation-like peaks of SPOF are remained very well. The computer simulation results are given. The comparison of the correlation outputs of BSPOF with that of SPOF is discussed. And 3-D plots of correlation output are presented.