"Echo State" neural networks (ESN), which are a special case of recurrent neural networks, are studied with the goal to achieve their greater predictive ability by the correction of their output signal. In this paper standard ESN was supplemented by a new correcting neural network which has served as an autoregressive predictor. The main task of this special neural network was output signal correction and therefore also a decrease of the prediction error. The goal of this paper was to compare the results achieved by this new approach with those achieved by original one-step learning algorithm. This approach was tested in laser fluctuations and air temperature prediction. Its prediction error decreased substantially in comparison to the standard approach.