By assuming that (1) the decay $K_1\to \gamma \gamma$ is saturated by the $2\pi$ intermediate state, (2) the $K\pi \pi$ vertex is of the first-order weak interaction, and (3) the $\pi \pi \to \gamma \gamma$ process goes by exchanges of $\rho$, $\omega$, and $\phi$, the contributions to the decay rate of $K_1\to \gamma \gamma$ from the three exchanges are calculated. It is found that the contributions do not alter in any significant way the result of the perturbation calculation using the Born term for the $\pi \pi \to 2\gamma$ reaction.

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