Proper motions in penumbra have been measured using local correlation tracking techniques in a high spatial resolution series of images (˜0.12 arcsec). Assuming these motions to trace true plasma motions, we have detected converging flows that arrange the plasma in long narrow filaments mostly placed along dark penumbral filaments. These converging flows suggest downflows in the filaments of ˜ 200 m s-1. We interpret the association between downflows and dark features as a sign of convection that, once several observational biases are considered, could transport enough energy to balance the radiative losses of penumbra.