The present paper discusses a method for robust face recognition that works even when only one image is registered and the test image contains a lot of local noises. Two types of facial image decomposition are compared both theoretically and experimentally. That is, we consider both a projectional decomposition, in which images are decomposed into individuality and other components, and a locational decomposition, in which the effects of local noises are suppressed. These two decompositions are simple and powerful and can be applied in collaboration with one another. This collaboration can be realized in a straightforward manner because the decompositions are consistent with one another. They work in a complementary manner and provide better results than when the decompositions are used independently. Finally, we report experimental results obtained using three databases. These results indicate that the combination of projectional and locational decompositions works well, even when only one image is registered and the test images contain significant noise.