Abstract: Based on the expansion of the window function of a hard edge aperture into a finite sum of complex Gaussian functions,the recurrence propagation equation of cosh Gaussian(ChG)beams through a multi apertured paraxial ABCD optical system is derived,which permits us to study the propagation of ChG beams through hard edge optics analytically.Numerical results are given and compared with those derived by the straightforward integral of the Collins formula,which shows the advantage of saving the computer time greatly by means of our analytical formula.