Let $R=K[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $K$ and $I$ be a matroidal ideal of $R$. We show that $I$ is sequentially Cohen-Macaulay if and only if the Alexander dual $I^{\vee}$ has linear quotients. As consequence, $I$ is sequentially Cohen-Macaulay if and only if $I$ is shellable.

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