In [1] and [2], we studied the problem of the existence and uniqueness of a solution to some general BSDE on manifolds. In these two articles, we assumed some Lipschitz conditions on the drift f (b, x, z). The purpose of this article is to extend the existence and uniqueness results under weaker assumptions, in particular a monotonicity condition in the variable x. This extends well-known results for Euclidean BSDE.