Interferometric synthetic aperture radar presents a new technology for performing high-resolution topographic mapping. One of the factors critical to mapping accuracy is phase unwrapping. This paper presents a new algorithm that unwraps phase through fringe-line detection. The algorithm is effective in preventing error propagation, it preserves the image resolution, and, in the mean time, it produces negligible local errors. An edge-segment linking approach and a curve-fitting approach are investigated, and their performances are compared. Test results of the algorithm are shown with the actual interferometric SEASAT synthetic aperture radar images over large-relief terrain near Yellowstone National Park with a short baseline, and results are shown over relatively flat terrain in Death Valley of California with a long baseline.