An iteration algorithm for the analysis of speckle interference patterns is presented. First, four digitized phase-shifted patterns are locally averaged. The phase information is then extracted by the usual phase shift algorithm. The wrapped phase is in turn used to reconstruct four new phase-shifted patterns. These three steps form a cycle. Repetition of the three steps has a great effect on suppressing speckle noise. Theoretical study shows that the iterated phase converges to a perfect result under ideal conditions. In general, the iteration causes little error but improves the phase information a great deal. The signal-to-noise ratio rises when additional iterations are performed.