  The notion of $\mathcal{H}$-matroids was introduced by U. Faigle and S.
Fujishige in 2009 as a general model for matroids and the greedy algorithm.
They gave a characterization of $\mathcal{H}$-matroids by the greedy algorithm.
In this note, we give a characterization of some $\mathcal{H}$-matroids by rank
functions.
