In this paper,we present a novel procedure for the synthesis of a filter having an arbitrarily specified amplitude transmittance. The filter configuration consists of N birefringent stages placed between a polarizer and an analyzer, with each stage containing an identical section and a variable section. An additional variable section is placed in front of the analyzer. The synthesis procedure is based on the resolution of a generalized nonlinear equation system directly deducted from the Jones matrix formalism to determine the angles of each stage, the angle of the analyzer and the phase shifts of the variable sections. A typical example of a 6-stage birefringent filter having an arbitrarily non-symmetric amplitude transmittance is shown and the opto-geometrical parameters are given to demonstrate the efficiency of the proposed synthesis procedure. The results obtained show an excellent agreement with those developed in the literature