Highly strained films of BiFe0.5Mn0.5O3 (BFMO) grown at very low rates by pulsed laser deposition were demonstrated to exhibit both ferrimagnetism and ferroelectricity at room temperature and above. Magnetisation measurements demonstrated ferrimagnetism (TC ∼ 600K), with a room temperature saturation moment (MS ) of up to 90 emu/cc (∼ 0.58 μB /f.u) on high quality (001) SrTiO3. X-ray magnetic circular dichroism showed that the ferrimagnetism arose from antiferromagnetically coupled Fe3+ and Mn3+. While scanning transmission electron microscope studies showed there was no long range ordering of Fe and Mn, the magnetic properties were found to be strongly dependent on the strain state in the films. The magnetism is explained to arise from one of three possible mechanisms with Bi polarization playing a key role. A signature of room temperature ferroelectricity in the films was measured by piezoresponse force microscopy and was confirmed using angular dark field scanning transmission electron microscopy. The demonstration of strain induced, high temperature multiferroism is a promising development for future spintronic and memory applications at room temperature and above.