Summary: A partial ordering of monotone dependence on the class of nonnegative bivariate random variables with given marginals is defined, based on the notion of generalized Lorenz curve of the regression function. The relations with other monotone dependence orderings are examined, with particular attention to the EQD ordering proposed by T. Kowalczyk and E. Pleszczyńska [Ann. Stat. 5, 1221-1227 (1977; Zbl 0374.62051)]. Finally, a real valued parameter coherent with the introduced ordering is suggested.