We examine the long-run relation linking the demand for money in Australia to economic activity and the interest rate for an extended period from 1976 to 2010. Using the Johansen cointegration test, we test the relationship for three measures of monetary aggregate – currency, M1 and M3. The results provide evidence for a long-run equilibrium relation linking the demand for M1 to economic activity and the interest rate. The relationship is stable with unitary income elasticity and sizeable interest rate semi-elasticity. The evidence may open a new debate for the Reserve Bank of Australia to look into the use of M1 as a tool in implementing its monetary policy after a long-time abandonment of M3.