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Small systems consisting of particles interacting with long-range interaction exhibit a behavior depending enormously of its size and shape. We study an ultrathin magnetic film in square geometry by means of an Ising model with ferromagnetic interactions J and antiferromagnetic dipolar interaction G, which is characterized by the parameter d=J/G. It is well known that at low temperatures  there are an antiferro phase (for low d) and an stripes phase for (high d).In this work, varying the parameter d, we analyze exhaustively the configurations that minimize the energy in small squares of side L with open boundary conditions (with L < 9 ). Depending on the value of d, we found several ground states different from the antiferro and stripes states, all of these with at least one symmetry axis. We extend our study to bigger lattices and we found that these new phases are stables and remain with lower energy than the antiferro and stripes phases.Also, by means of a related model with short range antiferromagnetic interaction, we study which of these new phases can be due to the long-range interaction.