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A robust numerical solution to the inverse kinematics is proposed based on the Levenberg-Marquardt (LM) method, where the squared norm of residual of the original equation with a small bias is used for the damping factor. A rather simple idea remarkably improves the numerical stability and the convergence performance, even in unsolvable cases. Discussion is done through an investigation of the condition number of the coefficient matrix. Comparison tests with conventional methods show that only the proposed method succeeds in all cases. It frees operators from being careful about the target position-orientation assignment of effectors so that it facilitates easy robot motion designs and remote operations.