It includes the stages of a) Slicing that product in slices with a 5 determined thickness, b) Partially drying those slices with a pressure lower than the atmospheric pressure and, optionally, with a simultaneous energy supply, c) Applying a modified atmosphere to the 10 product, d) Maturing that sliced food product in that modified atmosphere and in a controlled temperature. This process allows to reduce considerably the time elapsed in the stages of drying and maturing food 15 products.