Given a pair of absolutely continuous random variables (X, Y) distributed as the generalized Farlie-Gumbel-Morgenstern (GFGM) distribution, we develop a test for testing the hypothesis: X and Y are independent vs. the alternative; X and Y are positively (negatively) quadrant dependent above a preassigned degree of dependence. The proposed test maximizes the minimum power over the alternative hypothesis. Also it possesses a monotone increasing power with respect to the dependence parameter of the GFGM distribution. An asymptotic distribution of the test statistic and an approximate test power are also studied. (c) 2006 Elsevier B.V. All rights reserved.