This paper proved, for the first time, that in a optical fiber with arbitrary index profile ,which have not any geometrical axes in cross section and changes randomly in longitudinal section, there are a couple of orthogonal axes, called as Principle Polarization Axes(PPA). If a linear polarized light inject from one input PPA, it keeps linear polarization out of an output PPA. Their additional phase shift produced by U matrix are opposite. So, this paper suggests, that we can take the group delay difference of them as PMD (Polarization Mode Dispersion),and the formula is given. In the practical measurement system, linear polarizer are used at both end of a fiber. Because PSP(Principle State of Polarization) is not a linear polarization state, the analyses of this paper maybe even approximate to real results.