A new stochastic gradient adaptation algorithm based on the cost function E[|ek|T], where T ≥ 2.0, and is a rational number, is proposed. Conditions for the convergence in the mean of the adaptive algorithm are derived along with the stability bounds on the step size μ. Merits of the new adaptation algorithm as compared with that of the least mean square (LMS) algorithm are demonstrated by means of simulations. Computer simulations were performed with non-Gaussian binary and quaternary sequences of data. Simulations are performed in the presence of far-end signal sequences of various attenuation levels in data echo cancellers for full duplex digital data trans mission over telephone lines. Three different echo path models were used in these simulations along with four attenuation levels for the far-end data sequences. Convergence goals were set 20 dB below the attenuation level of the far-end signals in each case. In a given set of simulations, T was increased starting from 2.0 in steps of 0.1 for each successive simulation as long as the algorithm remains convergent. It is observed that convergence time decreases with the increase in T initially and then levels off before increasing once again. These simulations indicate that a substantial reduction in convergence time can be achieved relative to the mean square algorithm. The amount of reduction in initial convergence time depends upon various parameters such as transfer function characteristics of the echo path, attenuation level of the far end signal and type of data. A set of simulations was also performed after introducing dispersion in the far-end signal in addition to the attenuation. Results of which show the same trend of reduction in convergence time with the increase in i, as for the case of attenuated only far-end signal. Although the superiority of the proposed algorithm is demonstrated for digital data echo cancellation only, it could be applied to various other areas of adaptive signal processing where data are non-Guassian.