Manganese (Mn)-based strong magnets have long been a challenge because their 3
d
half-filled nature, owing to the close proximity of Mn atoms, results in antiferromagnetic ordering. Among various Mn magnetic materials, L1
0
-MnAl (τ-phase) has received much attention since it shows ferromagnetism at a high Curie temperature despite the very short Mn–Mn distance. However, because of the difficult synthesis of the stoichiometric and perfectly ordered τ-phase, its intrinsic magnetic properties and mechanism are unclear. Here, we show the first observation of antiferromagnetism, having sixfold magnetic superstructure along the c-axis, in stoichiometric and chemically ordered τ-phase. Moreover, we found that super-exchange interaction between Mn atoms via
p
-electrons of Al atoms causes antiferromagnetism in τ-phase. The ferromagnetism in the conventional Mn-rich τ-phase results from the suppression of the super-exchange interaction due to the substitution the excess Mn atoms for the Al atoms. The current study of Mn-based magnetic materials mainly focuses on the lattice constant engineering based on the simple Beth-Slater picture of direct exchange. These findings present effective ways to obtain high magnetization without antiferromagnetic ordering.