A new phase measurement algorithm without phase-unwrapping problem is presented. It is mainly applied in the interferograms of few and straight fringes with noise and corrupted regions. Existing phase-unwrapping algorithms for those interferograms are trivial and time consuming. The new algorithm first searches N “seeding pixels” in the interferograms, then the interograms segmented into N parts by the “seeding pixels”. The adjacent “seeding pixels” phase difference is limited in the range of ［-π,π］. Because the phase measurement is relative, one can assume that one of the “seeding pixels” phase is a constant, and other “seeding pixels” phases can be easily obtained by the phase-stepping algorithm. Moreover, other pixels phases in the interferograms can be determined through the simple operation with the “seeding pixels” phases by means of the phase-stepping algorithm. A smooth flat mirror was measured in a Linnik interference microscope with phase-stepping interferometry. The interferograms were corrupted with many dirty spots or regions. The experimental results confirm that our new algorithm is fast and robust.