We present new results concerning the substellar binary population in the Orion Nebula Cluster (ONC). Using the Karhunen-Loève Image Projection algorithm, we have reprocessed images taken with the IR channel of the Wide Field Camera 3 mounted on the Hubble Space Telescope to unveil faint, close companions in the wings of the stellar point-spread functions. Starting with a sample of 1392 bona fide unsaturated cluster members, we detect 39 close-pair cluster candidates with separation 0"16-0"77. The primary masses span a range Mp ∼ 0.015-1.27 M☉, whereas for the companions we derive Mc ∼ 0.004-0.54 M☉. Of these 39 binary systems, 18 were already known, while the remaining 21 are new detections. Correcting for completeness and combining our catalog with previously detected ONC binaries, we obtain an overall binary fraction of 11.5% ± 0.9%. Compared to other star-forming regions, our multiplicity function is ∼2 times smaller than, for example, Taurus, while compared to the binaries in the field we obtain comparable values. We analyze the mass functions of the binaries, finding differences between the mass distributions of binaries and single stars and between primary and companion mass distributions. The mass ratio shows a bottom-heavy distribution with median value Mc/Mp ∼ 0.25. Overall, our results suggest that ONC binaries may represent a template for the typical population of field binaries, supporting the hypothesis that the ONC may be regarded as a most typical star-forming region in the Milky Way.