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Cloaking a static magnetic field is becoming a real possibility after the recently proposed concept of dc metamaterials. Here, we present, by a model based on superconductivity first principles, accurate and systematic calculations for the susceptibility of a dc metamaterial consisting of parallel square superconducting thin plates. Since both magnetic and kinetic energies are considered, our model takes into account the effect of a penetration depth in the superconductors and therefore can be applied for high-temperature superconductors. Thus, from the calculated results, a device that can cloak a static magnetic field may be constructed based on high-temperature superconducting thin films.