The dispersion vector analysis method based on Buchdahl model can be used to guide material selection and replacement in optical design to obtain material combinations with good achromatic effect, but at present the theory is only applied to the design of focused systems due to the limitation of mathematical form, and there is no precedent for guiding the design of unfocused systems. To further investigate the application of this theory to the unfocused system, a deformed expression of the dispersion vector scale factor applicable to the unfocused system is proposed, and the material selection of a seven-fold telescopic unfocused system is carried out by this method. The optimized system has a maximum chromatic aberration of only 2.705×10^-5D (Diopter) at 0.707 aperture. The focal shift difference between 632.8 nm and 1 064 nm wavelengths is 0.000 21 D, and the maximum focal shift in the wavelength range is only 0.004 7 D. The chromatic aberration of the system is effectively corrected, and the MTF of each field of view completely reaches the diffraction limit. The research results enable the dispersion vector analysis method based on Buchdahl model to be applied to the design of unfocused systems as well, providing a new idea for the selection of achromatic material combinations for unfocused systems.