The antiferromagnetic resonance in thin single-crystal plates of MnCO₃ was studied at omega _p/2 pi =9.3 GHz and T=4.2-10 K for large values of the angle theta between the static magnetic field H and the basal plane of the crystals. A set of quasi-equidistant absorption lines was observed for a wide range of magnetic fields H, which can be attributed to the size effect: the resonances of plane spin-waves with different wavevector values, mod k mod approximately=10⁵ cm^-1, standing perpendicularly to the crystal plate. The relaxation of the spin-waves was evaluated from the width of individual resonance lines, and found to amount to Delta omega _k/2 pi approximately=0.03 MHz at T=4.2 K.