Conventionally, the money demand function is estimated using a regression of the logarithm of money demand on either the interest rate or the logarithm of the interest rate. This equation is presumed to be a cointegrating regression. In this paper, we aim to combine the logarithmic specification, which models the liquidity trap better than a linear model, with the assumption that the interest rate itself is an integrated process. The proposed technique is robust to serial correlation in the errors. For the USA, our new technique results in larger coefficient estimates than previous research suggested, and produces superior out-of-sample prediction.