In this paper, a modified orthogonal forward regression (OFR) least-squares algorithm is presented for system identification and modelling from noisy regressors. Under the assumption that the energy and signal-to-noise ratio (SNR) of the signals are known or can be estimated, it is shown that unbiased estimates of the Error reduction ratios (ERRs) and the parameters can be obtained in each forward regression step. Examples are provided to illustrate the proposed approach.