Conclusions. ESO 456-SC38 adds to the list of moderately metal-poor globular clusters located in the inner bulge. It has a blue horizontal branch and is very old. The cluster is confined to the bulge and bar region, but it does not support the Galactic bar structure. The old stellar population represented by clusters like this has to be taken into account in models of Galactic bulge formation. Studying them also provides indications on the formation times of the globular clusters themselves.