This paper provides new evidence on the money demand function for Bangladesh using cointegration techniques and a longer quarterly time series data than previously used. Cointegration results indicate that a single co-integrating vector describes the long-run equilibrium money demand relationship in Bangladesh for both the narrow and broad money categories. It is also found that the money demand function is stable and is highly dominated by the transaction motive for holding money. The effects of alternative opportunity cost variables on money demand were not found to be significant. The short-run money demand function was found to be stable and the speed of adjustment to the long-run equilibrium was found to be reasonable for both money categories. The empirical results may have significant implications for monetary policy of the country.