In order to improve the accuracy, robustness, and computational load of c-means clustering models, a series of hybrid solutions have been proposed. Mixtures of fuzzy (FCM) and possibilistic c-means (PCM) clustering generally attempted to avoid the noise sensitivity of the former and the coincident clusters of the latter. On the other hand, mixtures of fuzzy and hard c-means (HCM) have been proposed to speed up fuzzy clustering without losing the quality of its partitions. In this paper, a novel hybrid c-means algorithmic scheme is proposed that unifies the objective functions of all three conventional clustering models. The strength of each component within the mixture is controlled by two tradeoff parameters. The optimization of the proposed objective function is achieved using the alternating optimization derived from zero gradient conditions and Lagrange multipliers. The novel hybrid's behavior is evaluated in terms of classification accuracy, cluster validity and execution time, using the IRIS data set. Suitably chosen tradeoff parameters enable the proposed algorithm to achieve better accuracy than previous models, while performing less computations.