  Non-Hermitian degeneracies are classified as defective and nondefective
exceptional points~(EP). While in defective EPs, both eigenvalues and
eigenenergies coalesce, nondefective EPs are characterized merely by the
occurrence of degeneracies in their eigenvalues. It is also known that all
degeneracies are either symmetry-protected or accidental. In this paper, I
prove that anti-unitary symmetries protect all nondefective twofold EPs. By
developing a 2D non-Hermitian tight-binding model, I have demonstrated that
these symmetries are composite of various symmetry operations such as discrete
or spatial point-group symmetries and Wick's rotation in the non-Hermitian
parameter space. Introducing these composite symmetries, I present the
protection of nondefective EPs in various parameter regimes of my model. This
work paves the way to stabilizing nondefective EPs and offers a new perspective
on understanding non-Hermitian band crossings.
