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The formalism of nonlinear realizations is used to construct a theory with$1/2$ partial breaking of global supersymmetry with the $N=(1,0)$, $d=6$abelian vector multiplet as a Goldstone superfield. Much like the case of the$N=2$, $d=4$ Born-Infeld theory, proper irreducibility conditions of themultiplet are selected by the invariance with respect to the externalautomorphisms of the Poincar\'e superalgebra. They are found in the lowestnontrivial order in the auxiliary field. The fermionic contributions to theBianchi identity are restored by assuming its covariance with respect to brokensupersymmetry. The invariance of the action with respect to unbrokensupersymmetry is checked in the lowest order in the fermionic fields. Thesupersymmetry preserving reduction of the $d=6$ action to four dimensions isperformed, resulting in the $N=4$, $d=4$ Born-Infeld theory. As expected, thereduced action enjoys $U(1)$ self-duality.

Component $d=6$ Born-Infeld theory with $N=(2,0)\rightarrow N=(1,0)$ supersymmetry breaking