In 1983, Atanassov extended the fuzzy set and originally introduced the concept of intuitionistic fuzzy set (IFS). The basic elements in every IFS are called intuitionistic fuzzy numbers, each of which consists of a membership degree, a non-membership degree and a hesitancy degree. Compared with the traditional fuzzy set, the IFS is more flexible and practical to deal with the ambiguity and uncertainty. In this paper, we first try to define the basis in intuitionistic fuzzy environment and then study some of its relevant properties. After that, we propose the coordinates based on the basis and present some theorems of the coordinates. Finally, we show how to find the smallest basis of any region.