The clustering approach is considered as a vital method for many fields such as machine learning, pattern recognition, image processing, information retrieval, data compression, computer graphics, and others. Similarly, it has great significance in wireless sensor networks (WSNs) by organizing the sensor nodes into specific clusters. Consequently, saving energy and prolonging network lifetime, which is totally dependent on the sensor's battery, that is considered as a major challenge in the WSNs. Fuzzy c-means (FCM) is one of classification algorithm, which is widely used in literature for this purpose in WSNs. However, according to the nature of random nodes deployment manner, on certain occasions, this situation forces this algorithm to produce unbalanced clusters, which adversely affects the lifetime of the network. To overcome this problem, a new clustering method called FCM-CM has been proposed by improving the FCM algorithm to form balanced clusters for random nodes deployment. The improvement is conducted by integrating the FCM with a centralized mechanism (CM). The proposed method will be evaluated based on four new parameters. Simulation result shows that our proposed algorithm is more superior to FCM by producing balanced clusters in addition to increasing the balancing of the intra-distances of the clusters, which leads to energy conservation and prolonging network lifespan.