When incorporating bending-warping deformation in the beam theory by using the higher-order kinematics, the warping function plays an essential role in establishing the decoupled constitutive relations. In this paper, the concept, orthogonality conditions and normalized condition are first proposed for the warping function. A procedure is then suggested to determine the normalized warping functions. Four typical different types of warping functions, that is cubic, sinusoidal, hyperbolically sinusoidal, and exponential, are eventually obtained, which agree with the previous results but via such a unified procedure. The rigidity coefficients in the constitutive relations are also evaluated to exhibit the higher-order nature of bi-moment and bi-shear.