Suppose N is a compact Riemannian manifold, in this paper we will introduce the denition of N-valued BSDE and L2(T^m;N)-valued BSDE for which the solution are not necessarily staying in only one local coordinate. Moreover, the global existence of a solution to N-valued BSDE or L2(T^m;N)-valued BSDE will be proved without any convexity condition on N. This talk is based on a joint paper with Wenjie Ye.