  We consider a superconducting film with Magnetic Dots Array (MDA) placed on
it. Magnetic moments of these dots are supposed to be normal to the film and
strong enough to create vortices in the superconducting film. Magnetic
interaction between dots is negligible. Below the superconducting transition
temperature of the film in zero magnetic field the MDA with randomly magnetized
dots produces resistive state of the film. Paradoxically, in a finite magnetic
field the film with MDA is superconductive.
