External cutting member which is configured to be used in a hair-cutting unit in combination with a rotatable internal cutting member having at least one hair-cutting edge for the purpose of subjecting a portion of skin to a hair-cutting action, wherein the external cutting member is generally cup-shaped and comprises a base and an annular wall extending from a circumferential area of the base , wherein, at an exterior side thereof, the base has an exterior base surface configured to face the portion of skin to be subjected to a hair-cutting action, and at an interior side thereof, the base has an interior base surface configured to face the internal cutting member , wherein the base includes at least one hair-cutting track which is annular about a central axis of the external cutting member and provided with a plurality of hair-entry openings , and an annular base portion located between a central portion of the base and an innermost one of the at least one hair-cutting track which is closest to the central axis , wherein, seen in a cross-section of the external cutting member comprising the central axis , the annular base portion is provided with a profiled section which is located between a straight inner section and a straight outer section of the annular base portion , which is annular about the central axis , and which is shaped according to a predefined profile, characterized in that the profiled section comprises a first bent connection zone at a location of connection to the straight inner section and a second bent connection zone at a location of connection to the straight outer section , and wherein, in an axial direction parallel to the central axis , the predefined profile of the profiled section involves an axial height difference (h) of at least one of the exterior base surface and the interior base surface of at least 80 μm over a radial measuring distance in the profiled section of at most 800 μm in a radial direction relative to the central axis . wherein the external cutting member is generally cup-shaped and comprises a base and an annular wall extending from a circumferential area of the base , wherein, at an exterior side thereof, the base has an exterior base surface configured to face the portion of skin to be subjected to a hair-cutting action, and at an interior side thereof, the base has an interior base surface configured to face the internal cutting member , wherein the base includes at least one hair-cutting track which is annular about a central axis of the external cutting member and provided with a plurality of hair-entry openings , and an annular base portion located between a central portion of the base and an innermost one of the at least one hair-cutting track which is closest to the central axis , wherein, seen in a cross-section of the external cutting member comprising the central axis , the annular base portion is provided with a profiled section which is located between a straight inner section and a straight outer section of the annular base portion , which is annular about the central axis , and which is shaped according to a predefined profile, characterized in that the profiled section comprises a first bent connection zone at a location of connection to the straight inner section and a second bent connection zone at a location of connection to the straight outer section , and wherein, in an axial direction parallel to the central axis , the predefined profile of the profiled section involves an axial height difference (h) of at least one of the exterior base surface and the interior base surface of at least 80 μm over a radial measuring distance in the profiled section of at most 800 μm in a radial direction relative to the central axis . <EOS>