In 2013, Ku and Wong showed that for any partitions $μ$ and $μ'$ of a positive integer $n$ with the same first part $u$ and the lexicographic order $μ\triangleleft μ'$, the eigenvalues $ξ_μ$ and $ξ_{μ'}$ of the derangement graph $Γ_n$ have the property $|ξ_μ|\le |ξ_{μ'}|$, where the equality holds if and only if $u=3$ and all other parts are less than $3$. In this article, we obtain an analogous conclusion on the eigenvalues of the perfect matching derangement graph $\mathcal{M}_{2n}$ of $K_{2n}$ by finding a new recurrence formula for the eigenvalues of $\mathcal{M}_{2n}$.