Abstract: The derivation mistake in Caos Fuzzy Fisher Criterion (FFC) based Semi-Fuzzy Clustering Algorithm (FFC-SFCA) is pointed out. Combining Fuzzy Compactness and Separation (FCS) clustering algorithm, a new clustering algorithm, FFC-FCS, is proposed in this paper. FFC-FCS make full use of the feature extraction and dimension reduction characteristics of FFC, alternately running FFC in the original data space and FCS in the projection space, clustering the original data is accomplished by clustering the dimension reduction data. FFC-FCS not only shows excellent capability of classifying low dimensional data but also has a certain grade classification advantage with respect to high dimensional data. The experimental results show that FFC-FCS has super performance over original FCS, FFC-SFCA and classical Fuzzy C-Means(FCM).