We present the optical design of the baseline solution for the telescope of the KLYPVE-EUSO UHECR experiment. The adopted optical layout is a Schmidt camera covering a field of view of 40° with an entrance pupil diameter of 2.5 m, a 4 m diameter spherical mirror and a focal length of 1.7 m. The resulting very fast relative aperture (F/# 0.7) minimizes the detector size and its obstruction, resulting in a throughput of 70% over the entire field of view. The optical design, with an optimized shape of the corrector plate, allows for a correction of the geometric and the chromatic aberrations in the spectral range from 337nm to 391nm. The resulting nominal polychromatic RMS spot size is well inside the dimension of pixel size (3mm) of the multi-anode PMT all over the field of view, providing a ground resolution of about 750m from the ISS orbit. The maximum geometric distortion is below 5%. The axial length of the camera and the position of the aperture stop have been optimized in order to meet the stringent requirements on vignetting and throughout.