Robotic manipulators can execute multiple tasks precisely at the same time and, thus, the task-priority scheme plays an important role in implementing multiple tasks. Until now, several algorithms for task-priority have been used in solving the inverse kinematics for redundant manipulators. In this paper, through the comparative study of existing algorithms, we will propose a new method for task-priority manipulation in terms of two important criteria -- algorithmic singularity and task error. This manipulation scheme will be applied to a planar three-link manipulator to demonstrate its effectiveness.