The change in the physic-mechanical characteristics and the strain by the martensitic mechanism in the heat-treated Cu–30.3 at.% Al–4.5 at.% Mn–5.1 at.% Co alloy are investigated. The melted alloy is subjected to homogenizing annealing at 973 K for 5 h and cooling with a furnace. Hardened samples are subjected to stepwise heat treatment: tempering at various constant temperatures in the 473–573 K range. It has been established, that during aging of the alloy in the 470–530 K temperature range, an increase in deformation occurs during MT, which may be a result of internal stresses relaxation during the Cu$_2$MnAl ferromagnetic particles precipitation during isostructural decomposition and facilitating the re-reintegration of martensite crystals at MT. It is shown that in the quenched and then aged at 473 K the Cu–Al–Co–Mn alloy sample, the strain during martensite transformation significantly exceeds that in samples of Cu–Al–Co and Cu–Al–Mn alloys of similar composition, subjected to the same treatment, which makes possible more efficient use of such alloys in industry.