Galactic open clusters do not survive long in the high-density regions of the inner Galactic disc. Inside the solar ring only 11 open clusters are known with ages older than 1Gyr. We show here, basing on deep, high-quality photometry, that NGC 4337, contrary to earlier findings, is indeed an old open cluster. The cluster is located very close to the conspicuous star cluster Trumpler 20, as well misclassified in the past, and that has received so much attention in recent years. NGC 4337 shows a significant clump of He-burning stars which was not detected previously. Its beautiful colour-magnitude diagram is strikingly similar to the one of the classical old open clusters IC 4651, NGC 752, and NGC 3680, and this suggests similar age and composition. A spectroscopic study is much needed to confirm our findings. This, in turn, would also allow us to better define the inner disc radial abundance gradient and its temporal evolution. To this aim, a list of clump star candidates is provided.