Some empirical findings in the literature regarding the two closely related areas of data reconciliation and state estimation for nonlinear dynamic systems suggest that the use of robust regression M-estimators is sufficient to implicitly cope with biased measurements. We present a counterexample to that belief on a dynamic model of two CSTRs in the presence of both measurement bias and outliers where such an approach gives rise to wrong transient behaviour of the reconciled values of the process variables. In the light of the above, we introduce and examine a method to deal simultaneously with outliers and explicitly with constant measurement bias. It is based on the location invariance for constant biased measurements assured by a robust estimator of scale, whereas for unbiased measurements the same robust estimator of scale is combined with a robust location estimator as a robustified version of the root mean square error. These two statistics are then combined together using the desirability function. Biased measurements are detected as a sequence of consecutive differences between measured and reconciled values of the same sign. Its performance is assessed numerically in the counterexample and compared with that of the correntropy M-estimator to show the superiority of the proposed data reconciliation method.