A systematic construction of fully-diverse, high-rate OFDM-based space-frequency coding schemes for the cooperative relay network communication is presented in this paper. Assuming an asynchronous communication between the intermediate relays and the destination node, it is shown that the proposed scheme can achieve full cooperative diversity for any possible time delays between the relays and the destination node if the number of subcarriers used in the OFDM modulation and the oversampling ratio used at the destination node are both powers of a prime. Such conditions are naturally met in all existing OFDM-based communication standards. Comparing to the space-time trellis codes proposed by Xia et al., the present scheme not only achieves full diversity gain at a much higher rate but also are more flexible in both code and signal designs. A design example targeting at the latest OFDM-based standards is also given.