Based on observations performed with the Pulkovo normal astrograph in 2008–2015 and data from sky surveys (DSS, 2MASS, SDSS DR12, WISE), we have investigated the motions of 1308 stars with proper motions larger than 300 mas yr⁻¹ down to magnitude 17. The main idea of our search for binary stars based on this material is reduced to comparing the quasi-mean (POSS2-POSS1; an epoch difference of ≈50 yr) and quasi-instantaneous (2МASS, SDSS, WISE, Pulkovo; an epoch difference of ≈10 yr) proper motions. If the difference is statistically significant compared to the proper motion errors, then the object may be considered as a Δμ-binary candidate. One hundred and twenty one stars from among those included in the observational program satisfy this requirement. Additional confirmations of binarity for a number of stars have been obtained by comparing the calculated proper motions with the data from several programs of stellar trigonometric parallax determinations and by analyzing the asymmetry of stellar images on sky-survey CCD frames. Analysis of the highly accurate SDSS photometric data for four stars (J0656+3827, J0838+3940, J1229+5332, J2330+4639) allows us to reach a conclusion about the probability that these Δμ binaries are white dwarf +Mdwarf pairs.