The V-system on
[0,1]constructed in 2005 is a complete orthogonal system. It has multiresolution property. This paper further studies the V-system of two variables. The orthogonal V-system of degree
defined over triangulated domains is presented. With the orthogonal V-system over triangulated domains, all the application of the V-system on
[0,1] can be generalized onto the surface. Especially, the triangulated surface represented by piecewise polynomial of two variables of degree
with multi-levels discontinuities can be precisely reconstructed by finite terms of the V-series.