A package comprises an entirety of a tray (10) having an open side and a ring-shaped cover rim (20) which is located at the open side of the tray (10), at an outer circumferential rim (16) of the tray (10), and which is connected to the tray (10) through a relatively weak breaking portion (30). For the purpose of manufacturing the package, a mold (41) is provided. Also, a sheet (40) is provided and placed in the mold (41), wherein a movement of the sheet (40) is forced in two different directions. The cover rim (20) is formed with an inner ring (21) in which an inward bulge (28) is realized, along at least a portion of the circumference thereof, as an aids in establishing a clamping connection between the cover rim (20) and the tray (10) once the cover rim (20) has been broken away from the tray (10).