Most observers have concluded that while money markets and government bond markets are rapidly integrating following the introduction of the common currency in the euro area, there is little evidence that a similar integration process is taking place for retail banking. Data on cross-border retail bank flows, cross-border bank mergers and the law of one price reveal no evidence of integration in retail banking. This paper shows that the previous tests of bank integration are weak in that they are not based on an equilibrium concept and are neither necessary nor sufficient statistics for bank integration. The paper proposes a new test of integration based on convergence in banks' profitability. The new test emphasises the role of an active market for corporate control and of competition in banking integration. European listed banks profitability appears to converge to a common level. There is weak evidence that competition eliminates high profits for these banks, and underperforming banks tend to show improved profitability. Unlisted European banks differ markedly. Their profits show no tendency to revert to a common target rate of profitability. Overall, the banking market in Europe appears far from being integrated. In contrast, in the U.S. both listed and unlisted commercial banks profits converge to the same target, and high profit banks see their profits driven down quickly.