This paper proposes a pair-wise approach to testing for output convergence that considers all N(N-1)/2 possible pairs of log per capita output gaps across N economies. A general probabilistic definition of output convergence is also proposed. The approach is compatible with individual output series having unit roots, does not involve the choice of a reference country in computation of output gaps, and can be applied when N is large relative to T. The test is applied to output series in the Penn World Tables (1950-2000), and to Maddison's historical series (1870-2000). Overall, the results do not support output convergence and suggest that the findings of convergence clubs in the literature might be spurious. However, significant evidence of growth convergence is found. Non-convergence of log per capita outputs combined with growth convergence suggests that there are important country-specific factors that render output gaps highly persistent.