Abstract: Algorithm singularity of the extended task-space method for kinematically redundant robot, which is one of the redundant solution method is studied deeply in the paper. Klein^2,4 and Cho^3,5 pointed out that if the extended task-space method is used for redundant robots, the distribution of algorithm singularities, caused by performance index functions and extended Jacobian matrix, should be determined in the joint space in order to avoid algorithm singularity. We have compared the optimal necessary condition of the performance index with the condition of algorithm singularity for the extended task-space method, and find that it is impossible for the method to cause algorithm singularity as the extended task-space method is used to solve the redundant prblems, therefore, it is not necessary to consider the problem of algorithm singularity.