Network coding signature (NCS) scheme is a cryptographic tool for network coding against pollution attacks. In [5], Chang et al. first introduced the related-key attack (RKA) to the NCS schemes and tried to give an instantiation of it. However, their instantiation is based on the random oracle (RO) model. In this letter, we present a standard-model instantiation. In particular, we prove that standard-model-based NCS scheme introduced by Boneh et al. in [4] (BFKW scheme, for short) can achieve Φ-RKA security if the underlying signature scheme is also Φ-RKA secure, where Φ is any family of functions defined on signing keys of NCS schemes.