We present 20 newly discovered candidates for binary systems with an RR Lyrae companion. Using the photometric data from the Optical Gravitational Lensing Experiment (OGLE) and Korea Microlensing Telescope Network (KMTNet) for the Galactic bulge, we searched for binary candidates among non-modulated fundamental-mode RR Lyrae variables. We constructed and investigated over 9000 O ？ C diagrams for individual pulsators, in order to find signs of the light-travel time effect. We found 20 variables exhibiting cyclic variation in the O ？ C (time of the observed minus calculated brightness maximum) diagram, which can be associated with a second component in the system, but for confirmation of binarity, a long-term radial velocity study is necessary. The modelling of the O ？ C diagrams yields orbital parameters, estimates of the semi-amplitude of the radial velocity curve, and the mass function. The orbital periods of our candidates range from 3 to 15 yr. Two of the binary candidates display a minimum mass higher than the assumed mass of the RR Lyrae component, which points towards an evolved companion that can under some circumstances contribute significantly to the total light of the system.