Making critical sections abortable is a promising approach to controlling priority inversions. To improve the schedulability of a system using abortions, the maximum number of abortions should be decreased. In this paper, we propose a real-time synchronization protocol named the selective abort protocol (SAP) which introduces a new abort scheme to the priority ceiling protocol. Our proposed scheme can make the maximum number of abortions smaller than with the conventional priority-based abort schemes. A method to determine an upper bound on the number of abortions under the SAP is presented, and schedulability analyses of systems using the protocol are illustrated. Some extensions of the SAP are also discussed.