The cubic interpolated pseudoparticle (CIP) scheme is one of the Japanese algorithms for solving partial differential equations, and it is proposed by Prof. Takashi Yabe. He has proposed various types of numerical schemes with the same name "CIP", and we discuss the original scheme proposed in 1985. The scheme is intended to be a highly accurate one for solving hyperbolic equations and is widely used in computational mechanics. It is well known as an accurate scheme but its stability analysis has been unsolved for long time. We give a weak stability estimate for the scheme applied to linear advection equations and also show that it is not strongly stable in L^2. This research is a joint work with Dr. Daiki Tanaka, Prof. Hiroshi Fujiwara and Prof Takaaki Nishida.