Abstract. The transformation of data from one grid system to another is common in climate studies. Among the many schemes used for such transformations is second-order conservative remapping. In particular, a second-order conservative remapping scheme first introduced in 1987 and extended in 1999 to work on the general grids of a sphere has, either directly or indirectly, has served as an important base in a variety of studies. In this study, the author describes a fundamental problem in the derivation of the method proposed by a pioneer study relating to the treatment of the centroid used as a reference point for the second-order terms in the longitudinal direction. In principle, use of the original formulation may cause damage to the entire remapping result. However, a method's native implementation software includes a preprocessing procedure that tends to minimize or even erase the error as a side effect in many, if not most, typical applications. In this study, three alternative formulations are proposed and tested and are shown to work in a simple application.