  The first non-trivial case of Hadwiger's conjecture for oriented matroids
reads as follows. If $\mathcal{O}$ is an $M(K_4)$-free oriented matroid, then
$\mathcal{O}$ admits a NZ $3$-coflow, i.e., it is $3$-colourable in the sense
of Hochst\"attler-Ne\v{s}et\v{r}il. The class of gammoids is a class of
$M(K_4)$-free orientable matroids and it is the minimal minor-closed class that
contains all transversal matroids. Towards proving the previous statement for
the class of gammoids, Goddyn, Hochst\"attler, and Neudauer conjectured that
every gammoid has a positive coline (equivalently, a positive double circuit),
which implies that all orientations of gammoids are $3$-colourable. In this
brief note we disprove Goddyn, Hochst\"attler, and Neudauers' conjecture by
exhibiting a large class of bicircular matroids that do not contain positive
double circuits.
