Spectropolarimetric observations of 96 chemically peculiar (CP) main-sequence stars have been carried out at the 6-m telescope at the Special Astrophysical Observatory of the Russian Academy of Sciences (SAO RAS) with the aim of searching for the presence of stellar magnetic fields. The stars selected for investigation were CP stars known to have strong anomalies in the wavelength region of the continuum flux depression around {lambda} 5200{AA}. This selection was conducted with the aid of low-resolution spectral observations, made with the SAO RAS 1-m telescope, and of published differential photometric data. Magnetic fields have been successfully detected in 72 stars of which only three stars were previously known to have magnetic fields. For two stars, the longitudinal component of the magnetic field B_e_exceeds 5kG: HD178892 - 7.4kG, and HD258686 - 6.7kG. We failed to reliably detect the magnetic field in the other 24 CP stars. These stars are mostly fast rotators, a feature which hampers accurate measurements of B_e_. It is demonstrated in this paper that selecting candidate magnetic stars by considering their photometric indices Z or {Delta}alpha}, or alternatively, by inspecting low-resolution spectra around the {lambda}5200{AA} flux depression, considerably increases the detection rate.