In this letter, we consider the inter-relay interference (IRI) problem for amplify-and-forward (AF) two-path successive relay networks. To reduce processing burden for IRI cancelation at the relay nodes, a novel precoding-based interference cancelation scheme based on row-space mapping is proposed, where a pair of orthogonal precoding matrices is alternately utilized to project the source data onto the null space of the received data that is independent of channel state information (CSI). By designing a combined decoding and re-encoding scheme, both the IRI signal and accumulated noise are perfectly suppressed at the relay nodes. Simulation results show that the proposed scheme is significantly better than the channel estimate based interference cancelation schemes.