This paper deals with the formulation of a manipulator Jacobian based Newton-Raphson algorithm for robot inverse kinematics. A strict descent feature has been incorporated into the algorithm to make it robust. Previous studies with Newton-Raphson type matrix iteration have produced an overdetermined system of linear equations which relates small changes in the joint variables. Dealing with these extra equations led to computational inefficiency. Previous manipulator Jacobian based predictor-corrector algorithms for inverse kinematics avoided this inefficiency, but these required either a variable time step or a small fixed time step; also special attention was required to start these algorithms. Motivated by the advantages of these two methods, this paper presents a robust manipulator Jacobian based Newton-Raphson algorithm for robot inverse kinematics.