The conventional computational algorithms for full information maximum likelihood (FIML) estimation of the censored probit model (see Farber, 1983), will sometimes fail to converge when the estimated value of the correlation coefficient (ñ) approaches ±1; even when the true value of ñ is not at a boundary. We show that a simple reparametrization of the censored probit model may afford straightforward Newton-Raphson convergence to the true FIML estimate for cases in which likelihood maximization under the conventional censored probit parameterization would have failed. Moreover, our method avoids the computational and inferential complications that arise in alternative methods that, based on a specified criterion, suggest fixing the estimated value of ñ at -1 or +1. For the purpose of illustration the method is used to estimate the determinants of elderly parents’ receipt of informal care from their children.