We present a novel algorithm based on a hybrid of the global and local treatment of a wrapped map. The proposed algorithm is especially effective for the unwrapping of speckle-coded interferogram contour maps. In contrast to earlier unwrapping algorithms by region, we propose a local discontinuity-restoring criterion to serve as the preprocessor or postprocessor of our hybrid algorithm, which makes the unwrapping by region much easier and more efficient. With this hybrid algorithm, a robust, stable, and especially time effective phase unwrapping can be achieved. Additionally, the criterion and limitation of this hybrid algorithm are fully described. The robustness, stability, and speed of this hybrid algorithm are also studied. The proposed algorithm can be easily upgraded with minor modifications to solve the unwrapping problem of maps with phase inconsistency. Both numerical simulation and experimental applications demonstrate the effectiveness of the proposed algorithm.