Non-stationary MHD interaction of a horizontal magnetic field with a three-dimensional cellular convection is studied by means of computational methods and methods of mean field electrodynamics.For a given magnetic field drop across the convective layer, the rate of magnetic flux penetration through this layer is characterized by two integral coefficients: the first one describing the topological pumping effect arises from the antisymmetric part of the α-effect, while the second coefficient accounts for the enhancement of the effective diffusion due to the convective motions. In the magnetic-Reynolds-number range studied (−5 [les ] Rm [les ] 5) these coefficients are found to be, correspondingly, odd and even functions of Rm only. The net magnetic flux escape rate into vacuum decreases at Rm > 2·2 when compared with a case of a layer without cellular motions. Here the topological pumping prevails not only over the convective enhancement of diffusion but begins to suppress even the background diffusion action.Thus, the asymmetry in the transport properties of cellular motion is again demonstrated, and their difference from those of random turbulence is identified.