Thirty years after the discovery of brown dwarfs, the search for these objects continues, particularly in the vicinity of the Sun. Objects near the Sun are characterized by large proper motions, making them seen as fast-moving objects. While the Gaia DR3 catalogue is a comprehensive source of proper motions, it lacks the depth needed for discovering fainter objects. Modern multi-epoch surveys, with their greater depth, offer a new opportunity for systematic search for ultracool dwarfs. The study aims to systematically search for high proper motion objects using the newly released catalogue of epochal WISE data in order to identify new brown dwarf candidates in the solar neighborhood, estimate their spectral types, distances and spatial velocities. We used recently released unTimely catalogue of epochal detections in unWISE coadds to search for objects with high proper motions using simple motion detection algorithm, combined with machine learning based artefact rejection routine. This method was used to identify objects with proper motions exceeding approximately 0.3 arcseconds per year. The identified objects were then cross-referenced with data from other large-scale sky surveys to further analyze their characteristics. The search yielded 21885 moving objects with significant proper motions, 258 of which had not been previously published. All except 6 of them are compatible with being ultracool dwarfs. Among these, at least 33 were identified as most promising new T dwarf candidates, with estimated distances closer than about 40 parsecs, and effective temperatures less than 1300K.