An algorithm is developed for solving the inverse kinematic problem of a 6-degree-of-freedom robot with a wrist offset for which the closed form inverse solutions are not obtainable, but knowledge of one joint variable allows closed form solutions of the remaining joint variables. The algorithm does not require Forward Kinematics nor Jacobian but uses the implicit kinematic relationships between joint variables and the given hand position. An iterative back substitution method is used to solve the inversion and the optimal conditions of the convergence are incoporated. An example is given to illustrate the concepts, the solution procedure and its convergency.