We have investigated magnetism of $Fe_2 /Ir_4$(001) superlattice in terms of a first-principles calculation by using an all-electron full-potential linearized augmented plane-wave (FLAPW) method within the generalized gradient approximation (GGA). We considered two magnetic states, the ferromagnetic (FM) and antiferromagnetic (AFM) coupled states between the Fe layers. It was found that the FM state was energetically more stable than the AFM one by 0.166 eV. Calculated magnetic moments of the Fe layers were, in absolute values, 2.45$mu_B$ and 2.30 $mu_B$for the FM and AFM states, respectively. We also found that the Ir layers had very small magnetic moments less than 0.1 $mu_B$ for both magnetic states. In all the magnetic states, the subinterface Ir layers were coupled antiferromagnetically to the interface Ir layers, while the interface Ir layers were always coupled frerromagnetically to the interface Fe layers. These results contradicted to recent experimental reports of magnetically "dead"Fe layers in Fe/Ir superlattices for which the Fe layer thickness was less than two atomic layers. We attributed that the experimentally observed "dead"Fe layers were due to possible interdiffusion between Ir and Fe layers.en Ir and Fe layers.