The standard deviation of metropolitan per capita personal income (PCPI) and metropolitan average wage per job (AWPJ) provide straightforward indicators of unconditional sigma convergence for metropolitan economies within the United States. Using data for all metropolitan areas in the continental United States for the period 1969-2001, we tested for the unconditional sigma income convergence hypothesis by applying two unit root tests to the time series of the two standard deviations. Our results indicate that the time series can be described as random walks with drift, thereby supporting the claim that income divergence among metropolitan economies is not decreasing.