Beamforming is a common technique used to increase signal gain in communication networks. We developed an efficient 1-bit feedback beamforming algorithm that runs in time proportional to the number of transmitters in the network. There are 2 variable parameters in the algorithm: the probability of any transmitter changing its phase in the next iteration, and the amount by which a transmitter is permitted to change its phase in a single iteration. The parameters producing the optimal running times were discovered through numerical stimulations in MATLAB. We then analyzed the running time of the algorithm mathematically and showed that the lower bound of the running time of our proposed algorithm is linear in proportion to the total number of transmitters. Our work provides a basis for future development of beamforming algorithms that are more robust to noise.