In this paper, we present a novel non-iterative coordinated beamforming algorithm for overlaid multicell coordinated beamforming systems where a macro base station acts as an anchor and computes the beamforming vectors. We propose beamforming vector design that improves the received signal-to-interference-plus-noise-ratio while reducing the computational complexity. We also show its asymptotic behaviors with respect to the number of antennas, confirming that the proposed solutions are useful for large-scale multiple-input multiple-output systems in heterogeneous and small cell networks.