This article presents a blending method for basic curves including conics and circle arcs. The explicit formulas of basic curves represented by C-type spline of degree 2 was derived. The whole blending curve is $C^1$-continuous. Comparison with the blending method by rational $G^2$ splines which is rational splines of degree 3, the proposed method is simpler to represent and blend basic curves. Further, we design a subdivision method to generate the blending curve which is exact for those segments of basic curves and approximative for those segments of blending. By the theory of asymptotic equivalence, we also proved the $C^1$-continuity of proposed subdivision curves.