We present a study of the properties of short Gamma-Ray Bursts (GRB) as observed by the Gamma-Ray Burst Monitor (GBM) on-board the Fermi space telescope. The GBM observes about 45 short GRB per year, five of which have been detected above 100MeV by the Large Area Telescope (LAT) over the first three years of Fermi operations. In this work, we aim to understand if the high-energy emission observed in short bursts is related to a hard spectral component in the prompt phase and/or to a long-lasting emission, two properties of bright long and short GRB observed by Fermi (e.g. 090510A, 090926A, 090902B). We consider short GRB from the first two GBM catalogs, covering four years of observations, and compare GRBs with LAT detections to those with non-detections. We will also study the link between this high-energy emission and the spectral characteristics measured in the energy range covered by the GBM.