Inference for detecting the existence of an association between a diallelic marker and a trait locus is based on the chi-squared statistic with one degree of freedom. For polymorphic markers with m alleles (2), three approaches are mainly used in practice. First, one may use Pearson's chi-squared statistic with m-1 degrees of freedom (d.f.) but this leads to a loss in test power. Second, one can select an allele to be the most associated and then collapse the other allele categories into a single class. This reduces in a biased way, the locus to a diallelic system. Third, one may use the Terwilliger [J.D. Terwilliger, Am. J. Hum. Genet. 56 (1995) 777] likelihood ratio statistic which has a non-standard unknown limiting probability distribution. In this paper, we propose a new statistic, L(D), based on the second testing approach. We derive the asymptotic probability distribution of L(D) in an easy way. Simulation studies show that L(D) is more powerful than Pearson's chi-squared statistic with m-1 d.f.