It is shown how the recursive least squares (RLS) algorithm can be modified to compensate for a priori known errors of linearity in the output measurement, A novel signal model is used for this purpose. Only the nonlinear effects are modeled by an output error model, and much of the output measurements are used directly in the regression vector. The main benefit with this approach is that the advantages of the RLS, like quick initial convergence for infinite impulse response (IIR) models, can be retained for small linearity errors. At the same time the output nonlinearity is allowed to be noninvertible. This can be important to treat, for example, small deadzones and also to avoid the amplification of additive measurement disturbances. Such amplification can result from inversion of the output nonlinearity. Simulations illustrate the performance of the algorithm.