In the implementation of subdivision scheme, three of the most important issues are smoothness, size of support, and approximation order. Our objective is to introduce an improved ternary 4-point approximating subdivision scheme derived from cubic polynomial interpolation, which has smaller support and higher smoothness, comparing to binary 4-point and 6-point schemes, ternary 3-point and 4-point schemes (see Table 2). The method is easily generalized to ternary (2n + 2)point approximating subdivision schemes. We choose a ternary scheme because a way to get smaller support is to raise arity. And we use polynomial reproduction to get higher approximation order easily. Ó 2007 Elsevier Inc. All rights reserved.