In this paper, a limited-feedback decode-and-forward cooperative network with multiple relays is considered where each relay is equipped with multiple antennas. To combat error propagation, each multiple-input multiple-output relay participates in relaying phase, according to its received signal-to-noise ratio. In our scheme, space-time coding is independently employed at each relay. At relay, the detected symbols are forwarded using a novel beamforming method proposed in this paper. In the proposed technique, relays employ only two-bit quantized phase information of the channel between relay and destination, which reduces the overhead of the feedback channel. Our results highlight that using a simple maximal ratio combining at destination, the received SNR after combining the space-time coded signals is enhanced significantly compared with other existing methods. We further investigate the bit error rate performance of the general family of M-ary modulation schemes and show that the proposed design attains full diversity order without any rate or bandwidth cost. Also, closed form expressions are derived for optimal threshold and end-to-end bit error rate of the system. Numerical results illustrate a good agreement between the analytical and simulation results.