We propose a simple cooperative diversity scheme for a communication system consisting of two cooperating nodes that receive a single channel state information (CSI) bit from the destination node. Essentially, the feedback bit tells which cooperating node has the strongest channel, and this information is used appropriately to obtain cooperative diversity. A simple linear receiver is proposed and its performance is shown to be very close to the maximum-likelihood performance. An upper bound on the average error probability is derived for binary phase-shift keying (BPSK) in flat Rayleigh fading channels under the assumption of ideal inter-user channel. In addition, through computer simulations, it is verified that the proposed scheme presents a good error performance when the inter-user channel signal-to-noise ratio is high or when the inter-user channel has a well-defined line-of-sight component. In other words, the new scheme becomes interesting when the cooperating nodes are close to each other. Comparisons with a cooperative scheme based on the Alamouti code are provided.