Abstract: It is established that a new existence and uniqueness result for the L1 solution to a multidimensional backward stochastic differential equations (BSDEs) with uniformly continuous generators,where the generator g satisfies the Osgood condition in y and the α-Hölder(0＜α＜1) continuity condition in z,and the ith component gt(t,y,z) of g only depends on the ith row of matrix z.