A package of fresh meat in which a meat product (14) is placed in a support element (6) and the package is closed by means of a film (3) of the double lid, comprising an inner film (15) oxygen permeable, in contact with food, and an external oxygen impermeable film (16), said double cap film being placed on the meat product and heat sealed to the periphery of the support element in order to force a confined volume (19) inside the package, in which the space (18) between the two facing surfaces of the cover films does not comprise any particulate material, characterized in that the package is closed under an atmosphere that has an oxygen content greater than that of the atmosphere and containing at least an amount of oxygen effective to inhibit the discoloration of the packed meat product in which the space (18) comprises a layer of air trapped between them and at least said film Internal oxygen-permeable ula (15), in contact with food, is heat shrinkable.
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