This paper considers the problem of blind adaptive equalization of single-input multiple-output IIR channels without requiring the channel diversity condition. That is, the parallel sub-channels in the fractionally sampled model can have common factors. We develop an equalizer based on IIR prediction of the received signal. The predictor parameters are estimated by using the recursive extended least squares (RELS) algorithm. It is proved that the adaptive equalizer is globally stable and the prediction error converges in a Cesaro sense almost sure (a.s.) (with probability one) towards a scalar multiple of the input symbol sequence