The well-known parsing algorithm for the context-free grammars due to Valiant ("General context-free recognition in less than cubic time", Journal of Computer and System Sciences, 10:2 (1975), 308-314) is refactored and generalized to handle the more general Boolean grammars. The algorithm reduces construction of the parsing table to computing multiple products of Boolean matrices of various size. Its time complexity on an input string of length n is , where is the number of operations needed to multiply two Boolean matrices of size n ×n, which is O(n ^2.376) as per the current knowledge.