  Let $M$ be an arbitrary matroid with circuits $\mathcal{C}(M)$. We propose a
definition of a derived matroid $\delta M$ that has as its ground set
$\mathcal{C}(M)$. Unlike previous attempts of such a definition, our definition
applies to arbitrary matroids, and is completely combinatorial. We prove that
the rank of $\delta M$ is bounded from above by $|M|-r(M)$, that it is
connected if and only if $M$ is connected. We compute examples including the
derived matroids of uniform matroids, the V\'amos matroid and the graphical
matroid $M(K_4)$. We formulate conjectures relating our construction to
previous definitions of derived matroids.
