Successive relaying has recently emerged as an effective technique for cooperative networks and provides significant improvements in bandwidth efficiency over traditional relaying techniques; however, to achieve full-diversity, the available successive relaying protocols generally assume noise-free sourcerelay and interference-free inter-relay channels. In this paper, a novel successive relaying protocol is proposed for N-relay wireless networks by removing these optimistic assumptions. The proposed protocol benefits from distributed space-time block codes (STBCs) with coordinate interleaving and relay selection. It achieves a diversity order of two and high transmission rate under realistic network conditions with single-symbol maximum likelihood (ML) detection. A general N-relay signaling protocol is presented, and specific design examples are given for N = 2, 3 and 4-relay cooperative networks. The average symbol error probability (ASEP) is analytically derived and shown to match with computer simulation results. It is also shown via computer simulations that the proposed scheme achieves significantly better error performance and is more robust to channel estimation errors than its counterparts given in the literature under realistic network conditions.