Bi-stable mechanisms are systems with two distinct stable equilibrium positions within their range of operation. They are capable of steadily staying in positions without external power input and require less energy to move to the next stable state because of their snap-through behavior. Diverse applications including switches, deployable structures, and reconfigurable robots can benefit from bi-stability characteristics. However, the complexity of implementation and the limitation of structure configuration have made it difficult to apply conventional bistable mechanisms to the structures that require rotational bi-stability. Thus, in this paper, we proposed an implementation method using cylindrical magnets for the rotational bi-stable mechanism. The proposed bi-stable mechanism consists of a revolute joint with two links; one is the rotational link and the other is the fixed link. It has rotational bi-stability through the magnetic force relationship between the array of magnets on each link. To identify the characteristics of the proposed bi-stable mechanism, a cylindrical permanent magnet is considered as an electromagnet model that consists of one ring with a virtual electric current. Consequently, the magnetic field of the cylindrical permanent magnet can be calculated using Biot-Savart law. Similarly, the magnetic force between two cylindrical permanent magnets of the electromagnet model is calculated using Lorentz force law. The criteria of the magnet array for symmetric bi-stability are proposed and the potential energy diagram of the rotation link is considered as the performance criterion to identify the stable state.