Priority Ceiling Protocol (PCP) is a well known synchronization protocol for hard real time systems. However, it has a problem of ceiling blocking which imposes a great hindrance to real time systems especially for those with mixed tasks. A novel protocol called the Conditional Abortable Priority Ceiling Protocol (CA-PCP) is proposed. It resolves the problem by incorporating a conditional abort scheme into PCP. The new protocol inherits all the desirable characteristics from PCP and Ceiling Abort Protocol (CAP) which is yet another modification on PCP. In the proposed CA-PCP, a silent period is defined to control the number of aborts. During the period, it is conditional abortable so as to make a balance between blocking and abort of the tasks dynamically based on the utilization of the systems in order to achieve a high schedulability. Performance study of the proposed protocol has been done through simulation. The performance results indicate that CA-PCP can significantly improve the performance of a system if the length of the abortable critical sections are well chosen.