Abstract—A new adaptive algorithm, called LLMS, which employs two Least Mean Square (LMS) sections in tandem, is proposed for different applications of array beamforming.     The convergence of the LLMS algorithm is analyzed, in terms of mean square error, in the presence of Additive White Gaussian Noise (AWGN) for two different operation modes; normal referencing and self-referencing. Computer simulation results show that the convergence performance of LLMS is superior to the conventional LMS algorithms as well some of the more recent LMS based algorithms, such as constrained-stability LMS (CSLMS), and Modified Robust Variable Step Size LMS (MRVSS) algorithms. It is shown that the convergence of LLMS is quite insensitive to variations in both the input signal-to-noise ratio and the step size used. Also, the operation of the proposed algorithm remains stable even when its reference signal is corrupted by AWGN noise. Furthermore, the fidelity of the signal at the output of the LLMS beamformer is demonstrated through the Error Vector Magnitude (EVM) and the scatter plot obtained.