A new type of antiferromagnetic spin arrangement, which is theoretically possible in the rutile type crystal and seems to be realized in polianite, MnO2, is proposed. This spin arrangement, which will be named the screw-type structure, consists of spins screwing along the four-fold crystalline axis. The stability ranges of this and other spin structures are studied, assuming three different exchange interactions. The magnetic properties of the screw-type structure, including the anisotropy energy due to dipolar interaction and that due to crystalline field, the susceptibility, the spin waves, and the neutron diffraction pattern, are studied. Neutron diffraction data for polianite obtained by Erickson (unpublished) can well be accounted for by the screw-type structure with a pitch of (7/2)c. The magnetic properties of the MnO2 crystal are discussed on the basis of this 7/2-pitch-structure.