We revisit the controversy of unstable money demand function in the U.S. with the Johansen (1991) cointegration framework improved by imposing Johansen (1995) restrictions on deterministic trends. We find that the unstableness and structural break in the interest elasticity of money demand identified in the 1980s are only associated with the simple-sum measure of money. The Divisia monetary aggregates, the alternative measures that relax the assumption of perfect substitution among monetary assets, warrant stable and negative long-run relationships with the costs of holding. We further find new evidence suggesting that the disturbance in demand for money is due to the behavior pattern of financial innovations, which are distinct from those of conventional monetary assets. The role of the substitution effect is unneglectable in the measurement of money when a quantity-theoretical approach of monetary policy is of concern.