We look for high-amplitude variable young stars in the open clusters and associations of the Orion Belt. We use public data from the ASAS-3 Photometric V -band Catalogue of the All Sky Automated Survey, infrared photometry from the 2MASS and IRAS catalogues, proper motions, and the Aladin sky atlas to obtain a list of the most variable stars in a survey area of side 5 deg centred on the bright star Alnilam (ǫ Ori) in the centre of the Orion Belt. We identify 32 highly-variable stars, of which 16 had not been reported to vary before. They are mostly variable young stars and candidates (16) and background giants (8), but there are also field cataclysmic variables, contact binaries, and eclipsing binary candidates. Of the young stars, which typically are active Herbig Ae/Be and T Tauri stars with Hα emission and infrared flux excess, we discover four new variables and confirm the variability status of another two. Some of them belong to the well known σ Orionis cluster. Besides, six of the eight giants are new variables, and three are new periodic variables.