Abstract: Using the basis change for four-valent vertices which are connected with the recoupling theorem two four-valent rescaled bases are obtained in the spin networks representation, and it is proved that the basis change is a unitary transformation. The graph and the symbol expressions of the recoupling matrix used in action of volume operator on rescaled basis are obtained with the graph calculation method. Finally the eigenvalues of the volume operator and the space quantization are discussed.

Key words: Spin networks representation, Volume operator, Basis change, Recoupling matrix.