One of the main tasks of KDTCM (knowledge discovery in Traditional Chinese Medicine) is discovering novel paired or grouped drugs in Chinese Medical Formula (CMF) database, which are special combinations of two or more drugs. Correlation mining is much effective because of the large number of correlation relationships among various kinds of drugs. However, an independent pattern might have much more probability than a correlated pattern to be a novel paired or grouped drug even if they have same support for the sake of the downward closure property of independence. Therefore, we mine frequent independent patterns and frequent correlated patterns synchronously. Notions of an independent pattern and a correlated pattern are given. An algorithm is developed for mining frequent independent patterns and frequent correlated patterns synchronously. Experimental results show the effectiveness and the correctness of the techniques developed in this paper. Experimental results also show the great necessity of mining independent patterns and correlated patterns synchronously.