Phase retarders usually exhibit strong wavelength dependence. For this paper, the design and characteristics of an achromatic cascaded system of birefringent plates were studied. The combination of three retarders in a series had been previously proposed by Pancharatnam, and he discussed the possibility of fabricating reasonably good achromatic quarter-wave plates with a suitable level of retardance. This combination, however, still shows substantial variation in terms of retardance within 500 to 700 nm. Here, the combination of four plates for the construction of an almost achromatic quarter-wave plate, which has a variation of only ± 1 degree over the wavelength spectrum of 500 to 700 nm, is proposed. Moreover, spherical trigonometric considerations have been used by Pancharatnam for obtaining the transmission characteristics of a cascaded system. We, however, used the succinct and relatively simple Jones matrix formalism to derive a general expression for the equivalent retardation of this combination. The proposed arrangement of four birefringent plates promises better achromatic combinations.