Based on special relativity, the formation mechanism of characteristic X\|ray was studied, and the influence of the spin-orbit coupling on the characteristic X\|ray wavelength was analyzed. A calculation formula of the X\|ray wavelength based on special relativity is obtained. Error analysis is carried out systematically for the calculation values of wavelength, and the rules of relative error are obtained. It is shown that the results of the calculation are very close to the experimental results, which have some reference meaning for spectrum analysis of characteristic X\|ray in application.