The present paper addresses the question whether the less developed states, namely; Kedah, Kelantan, Pahang, Perlis, Sabah, Sarawak and Terengganu are converging with the richer state of Selangor, using unit root test and cointegration approach to test for income convergence for the period 1970-2013. We tested convergence on per capita real GDP for the states involved and the results suggest that the less developed states have been converging to the state of Selangor for the period under study. We also identify two convergence clubs among the states. In this respect, the state government has an important role to play in enhancing growth by continuously providing stable economic environment for investment and other productive economic activities. Without the Five-Year Malaysia Plans, this convergence phenomenon could not have been achieved in Malaysia. To ensure further convergence can take place at a faster rate in the future, government efforts and policies to foster narrowing states' income disparity has to be enforced further.