It is known that the achievement of the decode-and-forward (DF) protocol for cooperative communications is critically based on the prerequisite that the relay forwards the source transmitted signals as faithfully as possible. This implies that the relay can mostly know the correctness of its decoded results. In this paper, we employ the idea of detection with erasure in relay to approach this prerequisite. An erasure region is set to minimize the cost function that is formulated based on a specially designed bit-error-rate (BER) expression for the cooperation network. Whenever the received signals fall into this region, the relay will not perform DF. Power allocation can be simultaneously optimized as well. Simulations show that its resultant BER can be quite close to that of the perfect DF scenario and better than the BER of most previously presented signal-to-noise ratio (SNR) threshold-based relaying schemes.