Spherical linear interpolation in Minkowski space has got a number of important applications in computer graphics, physics and kinematics. Spherical linear interpolation in Minkowski space involves the computation of trigonometric functions, which are computationally expensive. The computation will be fast since the implementation does not need to evaluate any trigonometric functions in the inner loop. Furthermore, no renormalization is necessary and therefore it is a true spherical interpolation in Minkowski space. We propose that incremental Slerp in Minkowski space. In this paper we demonstrate four different methods for incremental Slerp in Minkowski space.