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A complete and efficient algorithm is proposed for searching form-closure grasps of n-hard fingers on 3-D objects represented by discrete points. Both frictional and frictionless cases are considered. This algorithm starts to search a form-closure grasp front a random grasp using an efficient local search procedure until encountering a local minimum. The local procedure is based on the powerful ray-shooting technique and searches in the direction of reducing the distance between the convex hull corresponding to the grasp and the origin of the wrench space. When the distance reaches a local minimum value, the algorithm decomposes the problem into sub-problems according to the existence conditions of form-closure grasps. A search tree whose root represents the original problem is employed to guide the searching process. The sub-problems are represented as children of the root node and the same procedure is recursively applied to the children. Theoretical analysis has been conducted on completeness and computational complexity of the algorithm. The efficiency of this algorithm is demonstrated by numerical examples.