The formulae of Gaussian parameters between the relay lens and the(two-mirror) system are derived. They satisfy the condition of exit pupil of the IR system matching the cold stop of the IR sensor. Once the diameter of the cold stop and its distance to the image plane are confirmed, the Gaussian parameters of the relay lens and the two-mirror system must satisfy these formulae, then the exit pupil will coincide with the cold stop. The elimination of aberrations may be done by aspherization of the primary and secondary mirrors and one surface of the relay lens. In order to prove the efficiency of the derived formulae,(6 real) systems are solved. The diameter of the IR system is taken as 250 mm, the diameter of the cold stop is 5 mm, and the distance between the cold stop and the IR image plane is(20 mm.) The radius of curvature of the primary mirror has two values:(-1000 mm) and(-800 mm,) the focal length of the two-mirror system:(2000 mm,)(1500 mm) and(1000 mm.) So,there are 6 systems with different constructive data are calculated.