Coherence loss is a critical issue in interferometric synthetic aperture radar geodesy, particularly when short-wavelength radar images are used to monitor earthquake deformation, and it may result in isolated fringes in an interferogram. The conventional unwrapping algorithms may incompletely unwrap or wrongly estimate the integer jumps between isolated fringes. In this paper, we propose a novel method to connect the isolated fringes in earthquake slip inversion. We use multiple starting points to unwrap the interferogram and then solve the integer ambiguities among the starting points by a dislocation-model-based integer least squares estimator. This estimator allows us to provide a quantitative evaluation of the reliability of the integer solutions in terms of two indicators (the success rate and residual ratio). The algorithm is robust to a certain degree of data noise and fault geometry error, as tested. Simulated experiments and case studies demonstrate that the proposed method can give better unwrapping results than the conventional approaches such as the minimum-cost flow (MCF), statistical-cost network-flow algorithm for phase unwrapping (SNAPHU), and iterative forms of MCF and SNAPHU with the assistance of a slip model. The earthquake slip inversion therefore benefits from the more accurate unwrapping results.