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The purpose of this paper is to propose a novel cluster map based blind RBF equalizer for received signal constellation (RSC) independent channel. Without the channel estimator, firstly, a neural-gas algorithm is used to obtain the desired number of unlabeled RBF centers. Then these unlabeled centers are partitioned into appropriate subsets based on a cluster map generated from the known RBF equalizer structure. This process, which also can be viewed as the weight initialization, is implemented merely by several simple sorting operations. Finally, the weight is adjusted iteratively by a unsupervised least mean square (LMS) algorithm. Because of the effective weight initialization that comply with the underlying structure of the RBF equalizer, the proposed blind RBF equalizer achieves almost identical performance with the optimal RBF equalizer. The validity of the proposed equalizer is also demonstrated by computer simulations.