Antisite disorder is observed to have significant impact on the magnetic properties of the double perovskite Y2CoMnO6 which has been recently identified as a multiferroic. A paramagnetic-ferromagnetic phase transition occurs in this material at Tc75K. At 2K, it displays a strong ferromagnetic hysteresis with a significant coercive field of Hc15 kOe. Sharp steps are observed in the hysteresis curves recorded below 8K. In the temperature range 2K≤T≤5K, the hysteresis loops are anomalous as the virgin curve lies outside the main loop. The field-cooling conditions as well as the rate of field-sweep are found to influence the steps. Quantitative analysis of the neutron diffraction data shows that at room temperature, Y2CoMnO6 consists of 62% of monoclinic P21/n with nearly 70% antisite disorder and 38% Pnma. The bond valence sums indicate the presence of other valence states for Co and Mn which arise from disorder. We explain the origin of steps by using a model for pinning of magnetization at the antiphase boundaries created by antisite disorder. The steps in magnetization closely resemble the martensitic transformations found in intermetallics and display first-order characteristics as revealed in the Arrott's plots. © 2014 AIP Publishing LLC.