The path independent algorithm is one of the important phase unwrapping algorithms, and diverse types of least-squares phase unwrapping algorithms are used widely. Since least-squares phase unwrapping algorithm does not hold back the error diffusing in space, an accurate unwrapped phase cannot be obtained by this algorithm directly, which limits the applications of the algorithms. A novel accurate phase unwrapping algorithm and the corresponding theoretical analysis are presented by analyzing the error characteristics of least-squares phase unwrapping algorithm. The validity of this new algorithm is shown by simulation and experimental examples of unwrapping, and the obtained phase proves that this new algorithm is accurate.