We consider a thin superconducing layer with a magnetic field direction slightly tilted from the plane-parallel orientation. In such a situation, which generalizes the Fulde–Ferrell–Larkin–Ovchinnikov state, both paramagnetic and orbital pair-breaking effects must be taken into account. We minimize the quasi-classical free energy to obtain the stable order parameter structure near the upper critical field, extending previous work [J. Low Temp. Phys. 118 (2000) 91] with regard to magnetic field contributions. We find two-dimensional periodic states, characterized by Landau quantum numbers n>1 showing antivortices, e.g. a unit cell with three order parameter zeros (two vortices and an antivortex) carrying totally a single flux quantum. The underlying physical mechanism is different from a recent prediction of antivortices in mesoscopic samples of triangular shape [Phys. Rev. Lett. 86 (2001) 1323].