In 2013, Shim proposed a conditional privacy-preserving authentication (CPP-BAT) scheme for vehicular ad hoc networks (VANETs). Their scheme was designed to improve Jiang et al.'s binary authentication tree (BAT) scheme that claimed insecure against forgery attacks, replay attacks, and Sybil attacks. Unfortunately, we also found out that Shim's CPP-BAT is potentially insecure against non-repudiation attacks. In this short article, we address the issue and give our improvement to withstand the threat.