A fully-pipelined systolic array for computing the minimum variance distortionless response (MVDR) was first proposed by McWhirter and Shepherd. The fundamental concept is to fit the MVDR beamforming to the non-contrainted recursive least-squares (RLS) minimization. Until now, their systolic array processor is well-recognized as the most efficient design for MVDR beamforming. In this paper, we first point out the mistake by relating the MVRD beamforming and RLS minimization and then propose a new algorithm for the MVDR beamforming. Moreover, a fully parallel and pipelined systolic array for the newly proposed algorithm is presented and the square-root free implementation is also considered.