Using the knowledge of differential manifold, the linear space with the dimension of n on the real number field was researched. In linear space , the existence about a cluster of smooth functions satisfying the unit decomposition were pointed out, and a unit decomposition theorem was established. In addition, applying the unit decomposition theorem in the linear space with the dimension of 2, the existence was shown that the three continuous functions satisfying the unit decomposition were defined in arbitrary open convex body . The linear space was combined with differential manifold, and a new method was showed to research decomposition and related problem of functions in the general linear space.