A decision feed back equalizer provides two feedback routines for one symbol-preceding decided data. The signal space is separated into decidable areas and uncertainty areas. Within each of decidable area the distance between any point and the signal point is small. Within each uncertainty area the distance between any point and the signal point is large. If the symbol-preceding equalized signal is in a decidable area, the piece of decided data is fed back, as it is presumed to be correct. If the symbol-preceding equalized signal exists in an uncertainty area, the piece of decided data is not fed back, as it is presumed to be in error. Here the one piece data is selected from all the predicted symbol-preceding decided data so that the instant equalized data is now in the decidable area. This piece of decided data is now fed back.