The conjugate effect of current relaxation and of current-vortex sheet formation on the magnetorotational instability is explored in a conducting fluid. It is found that the relative amplification of the magnetic viscosity from marginal stability to the instability determined by the maximum growth rate is around 924% when resistive effects dominate, while the corresponding quantity is around 220% in the ideal limit. This shows that the conjugate influence is much more efficient to amplify the magnetic viscosity than just the effect due to the standard magnetic tension. It is also found that the magnitude of the magnetic viscosity is effectively enhanced by the conjugate influence. The results presented here may contribute to the understanding of the various processes that play a significant role in the mechanism of anomalous viscosity observed in Keplerian disks. It is argued that the new effect shall be relevant in thin accretion disks. It is also mentioned that the proposed formulation may be of interest for some theories of magnetic reconnection. Possible extensions of this work are suggested.