Abstract: An LMS algorithm based on one dimensional slice of fourth-order statistics is proposed and its recursive form is given. This algorithm can suppress the correlated Gaussian noises effectively, and its performance is better than the conventional autocorrelation-based LMS algorithm. The recursive form reduces the computational complexity, and it can meet the need of real-time processing. Simulation results are presented to demonstrate the effectiveness of this approach. The presented algorithm can be used to estimate multi-path coefficients in radar, sonar and communication systems.