Symmetric phase-only filter (SPOF) has been widely applied to image registration and recognition, and has been proved efficient for fingerprint verification. Fingerprint images have a characteristic that the dominant information is concentrated in an elliptic frequency band of their ridges in low frequency domain. However, the existent fingerprint verification methods based on SPOF do not take this characteristic into account. To improve the performance of SPOF for fingerprint recognition, an appropriate region of support (ROS) can be used to set the least significant frequency region to zero. By means of theoretical and experimental analysis, we have found the optimal ROS for SPOF that achieves the best discrimination power among all the possible ROSs. Experiments show that our optimal ROS-based SPOF is more efficient than the method of band-limited SPOF (BLPOC).