The new mechanism of x-ray generation by clusters at their irradiation by femtosecond laser pulses has been suggested. We develop photo-recombination theory for electrons which first leave atomic clusters due to the outer ionization and then go into the ground quantum state of the neighbouring charged cluster. The charged cluster field is considered as a quantum potential well. The conclusion has been made that non-dipole x-ray photons at the photo-recombination into charged clusters have an energy which is larger than that for the well-known photo-recombination on separate atomic ions inside the cluster.