We have measured the electron spectra of Ne clusters after excitation with photon energies around the 2s inner valence threshold. At two photon energies below threshold, a resonantly enhanced surplus of low kinetic-energy electrons is observed. The kinetic energy of the peak does not vary with the photon energy and is slightly larger than the transition energy of Interatomic Coulombic Decay (ICD) above threshold. This leads us to assume that an ICD-like process is present. In analogy to the Auger and the resonant Auger decay this new phenomenon is termed resonant ICD.