The search for binaries among low-massive stars is one of the main goals of the Pulkovo program of investigation of stars with large proper motions. The motions of 1308 stars with proper motions larger than 300 mas·yr-1 down to magnitude 17 were studied. While analysing, we used Pulkovo Normal Astrograph observations in 2008-2015 and different digital surveys (DSS, 2MASS, SDSS DR12, and WISE). The main idea of the search for binary stars is reduced to comparing the quasi-mean (POSS2-POSS1; an epoch difference of ≍50 yr) and quasi-instantaneous (2MASS, 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 ∆μ -binary candidate. As a result, 121 stars have been qualified as astrometric binary candidates. The brightest of them (12 stars) have been included in the program of speckle observations with the BTA (SAO RAS) and the 2.5-m telescope of CMO (SAI MSU). The binarity of the brightest of these stars, J1158+4239 (GJ 3697), has been confirmed. The weighted mean estimates of the pair parameters are ρ=286.5±1.2 mas and θ=230.24±0.16° at the epoch B2015.88248. The magnitude difference between the pair stars is ∆ m=0.55±0.03 (the filter with a central wavelength of 800 nm and a FWHM of 100 nm) and ∆ m=0.9±0.1 (the R filter).