The feasibility and limitation of directly using the Lissajous figure and ellipse fitting technology to correct the phase extraction error in generalized data reduction algorithm (GDRA) for phase extraction of randomly phase-shifted interferograms are analyzed and discussed. By combining Lissajous calibration technology, which represents the transformative process of Lissajous ellipse to circle (ETC), with advanced iterative algorithm (AIA) we propose a novel generalized phase shifting algorithm (GPSA), and here it is abbreviated as ETCI method. The phase distribution and phase shifts that extracted from randomly phase shifted interferograms by use of ETCI are more accurate and the whole process is far faster than AIA. Additionally, proposed method is less sensitive to non-uniform background intensity and modulation amplitude. Numerical simulations are conducted to evaluate the performance of ETCI, and some influential factors are elaborated. The experimental results further indicate proposed method is suitable for truly random phase shifted interferograms. (C) 2016 Elsevier Ltd. All rights reserved.