In this paper authors have addressed the problems associated with blind adaptation technique used for channel equalization purposes. Blind adaptation techniques shows very poor convergence property in contrast to the supervised techniques which uses training sequences e.g. least mean square algorithm. Gradient descent based algorithm is one of the widely used blind adaptation schemes for equalization purpose. The most commonly and widely used gradient descent based blind adaptation algorithm is the Constant Modulus Algorithm (CMA) which suffers from the same poor convergence property. Also constant modulus algorithm is phase blind. In this work, authors have presented a new modified CMA Algorithm for blind equalization. The modified update equation is based on logarithmic cost function. Matlab Simulation results proves the claimed fast convergence, better stability, low BER value as compared to the CMA algorithm in noisy environment.