The demand for money is a critical component in the formulation of and implementation of monetary policy. A well-defined and stable money demand function is a necessary condition for monetary policy to have predictable effect on the macroeconomic variables. This paper applies the advanced technique of cointegration to estimate the demand for money balances in the case of Bangladesh and evaluates stability of the equations. The analysis shows that there exist a long-run relationship between real money, real income, inflation, and interest rate that remains stable over time. The long-run properties emphasize that both inflation and interest rate have negative effects on real money demand, whereas real income has positive effects. The long-run relationship is finally embedded in a dynamic equilibrium correction model. The short-run dynamic parsimonious error correction models for both money demand functions were estimated and these were free from the conventional econometric problem faced by other studies. The stability of the equations and coefficients were highly encouraging.Money Demand, Unit Root Test, ECM, Bangladesh.