This paper presents a recent study on kinematic modeling of a remote-controlled active catheter. The tip steering motion of the catheter is actuated in a tendon-driven manner. Two antagonistic groups of tendon actuation realize the distal tip deflecting with two-degree-of-freedom (2-DOF) allowing it to reach a considerable large spatial workspace without catheter shaft rotation. However, when modeling such bending deformation, the sequential rotation approach is easily misapplied. We address this problem and introduce a novel and unified modeling methodology based on the concept of simultaneous rotation and the use of Rodrigues' rotation formula. An accurate model is created for robotic catheters and also can be generalized to common multi-tendon-driven continuum manipulators. It is essential in achieving accurate control and improving autonomous execution of command tracking tasks.