In this paper, we develop a switch and examine transmit diversity algorithm for spectrum sharing cognitive networks. We consider a cognitive network composed of a primary link that employs constant rate and constant power transmission scheme with automatic-and-repeat request (ARQ) protocol, while the secondary link is composed of a fixed power multiple-antenna secondary transmitter and a single antenna receiver. Our objective is to develop a low complex transmit diversity algorithm at the secondary transmitter that maximizes the performance of the secondary link in terms of the effective throughput while maintaining a predetermined maximum loss in the packet rate of the primary link. In achieving this objective, we develop an algorithm that selects the best antenna, which maintains the quality of the secondary link in terms of signal-to-noise ratio above a specific threshold, based on overhearing the acknowledgment (ACK) and negative acknowledgment (NACK) feedback messages transmitted over the primary link. We also develop closed form expressions for the bit error rates and the effective throughput of the secondary link.