Abstract We propose a modification of a Modarres–Gastwirth test for the hypothesis of symmetry about a known center. By means of a Monte Carlo Study we show that the modified test overtakes the original Modarres–Gastwirth test for a wide spectrum of asymmetrical alternatives coming from the lambda family and for all assayed sample sizes. We also show that our test is the best runs test among the runs tests we have compared. Keywords: runs testtest of symmetrygeneralized lambda familypower AMS Subject Classification : Primary 62G10Secondary 62G30