Wall-climbing robots are operated in 2D space since the robots are always attached to the wall to be operated, however the operating environments of the robots are generally 3D space for search and rescue, inspection, and exploration missions. Wall-to-wall transition capability is necessary for a climbing robot to extend the operating range from 2D to 3D spaces. This paper presents a separable modular design of a wall-climbing robot that has high capability of internal wall-to-wall transition. The robot is composed of two identical dry-adhesive track-wheel modules which are connected by a separable magnetic connector. During the transition, the front module moves to the target wall by using the rear module as a support. After the transition, the modules are separated and work as independent robots. The front module can return to the original wall by cooperation with the rear module. By the process, the wall-climbing robot can reach all the internal 3D space. Static analysis and experimental results are presented to verify the performance of the robot design. The proposed design has advantages in high transition capability and working efficiency from the separable design, and the design is going to be extend to have external transitioning capabilities.