The kinetics of registration of lipid domains in the apposing leaflets of symmetric bilayer membranes is investigated via systematic dissipative particle dynamics simulations. The decay of the distance between the centres of mass of the domains in the apposing leaflets is almost linear during early stages, and then becomes exponential during late times. The time scales of both linear and exponential decays are found to increase with decreasing strength of interleaflet coupling. The ratio between the time scales of the exponential and linear regimes decreases with increasing domain size, implying that the decay of the distance between the domains' centres of mass is essentially linear for large domains. These numerical results are largely in agreement with the recent theoretical predictions of Han and Haataja [Soft Matter, 2013, 9, 2120-2124]. We also found that the domains become elongated during the registration process.