The B-spline functions are used in this note to generate the constrained minimum time path for a robot manipulator. The interpolated path via B-spline functions is determined via a unique set of virtual knots so that the robot path can pass every intermediate knot and satisfy the boundary conditions. The local control property of the B-spline functions can also be utilized to simplify the involved computational complexities. Further, the flexible polyhedron search algorithm is used to generate the near minimum-time path with velocity, acceleration, and jerk constraints on every intermediate point. This new approach can indeed simplify the formulation and procedures for generating the near minimum-time cubic B-spline path. This method has been used successfully to generate the constrained minimum-time joint trajectories for PUMA 560 robot.