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We suggest that the decay modes of kaons with a pion and a pionium($\pi^+\pi^-$ atom) in the final state can constitute a not yet consideredbackground to the very rare decay $K\to\pi\nu\bar\nu$. In fact, a part ofpioniums may escape the decay region before decaying into two $\pi^0$s (or to$\pi^0\pi^0\gamma$ in the case of excited pionium). To illustrate theimportance of this background, we show that it may even explain, under someassumptions, the unexpected $K_L$ decay events that appeared in the KOTOexperiment.

Pionium as a source of false events in the $K\to\pi\nu\bar\nu$ decays