A novel phase unwrapping method is proposed that can be used in digital holograms, magnetic resonance imaging and synthetic aperture radar interferometry. Phase unwrapping is often an essential task for images with periodic phases, and its result directly affects the measurement precision. However, the path‐independent unwrapped results generally cannot be obtained owing to the inconsistencies of phase gradients, i.e. residues. A simple and efficient approach is provided to determine the connections of opposite‐sign residues by analysing the relationship between the phase gradients and the residues’ generation. After the determination of the connections, integrated the phase map and obtained the path‐independent phase unwrapping result by not crossing the connections and residues. The proposed method has efficiently reduced the computational complexity when compared with the traditional phase unwrapping methods. The effectiveness of the proposed method was proved by experimental results based on real and simulated data.