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A recent development in the literature has proposed a cosine modulated filter bank - based multicarrier modulation technique with blind equalization capability. However, convergence studies of the proposed blind equalizer has been carried out through computer simulations only. In this paper, we present a thorough study of the blind equalizer by analyzing its associated cost function in detail. We show that the blind equalizer cost function is characterized by two global minima and two local minima. The analysis shows that although there is a chance that the blind equalizer converges to near one of the local minima, the stochastic nature of the adaptation algorithm will eventually result in a drift of the algorithm and convergence towards one of the global minimum points.