This paper presents the general solution of noncircular uniform waveguides in an arbitrary coordinate system. It can be expressed as expi(+ΔβV)zE0(x,y),where V is a matrix depending uniquely on the angle θ between polarization principal axis (PPA) and coordinate axis. As a kind of application, we give the method to find , Δβ and V(θ) in the weak-guided fiber, whose distortion is smaller.It is easier to use it for analyzing the effect of birefringence decreasing due to the lognitudinal asymmetry in a fiber, compared with Jones matrix.