Abstract: Multiple outputs logic function is an important tool for constructing cryptog-raphy systems, and correlation immunity is a critical criterion in designing secure logic functions. In this paper, a very simple method is used to prove that two descriptions of cor-relation immunity of multiple outputs logic function are equivalent indeed. The correlation properties of a kind of keystream generator are analyzed, which is defined by multiple out-puts logic functions. It is found that this constructing method is wrong, which means that the immunity expected by the construction cannot be obtained. Walsh transform technique and linear sequential circuit approximation method are applied to find the weakness of this kind keystream generator respectively. That is to say the keystream generator constructed by this method is vulnerable.