Applicator for applying a eyeliner to the eyelids, comprising an applicator member, the latter having on its external surface a recess and an applicator tip narrowing both in terms of its thickness and its width, the applicator tip having a substantially flat main facet extending from the recess towards the distal end of the applicator member, the applicator comprising all the following features:. - the applicator member being made of a porous material that is a felt, - the main facet extending as far as the distal end, - the applicator member extending along a longitudinal axis, the main facet extending along an axis inclined at an angle α relative to the longitudinal axis, the angle α being between 0 and 45°, - the width 1 of the main facet decreasing towards the distal end of the applicator member, the maximum width lmax of the main facet being between 2 mm and 5 mm, - the longitudinal axis Z of the main facet and the recess forming an angle η of between 30° and 145° between one another at their junction, - the recess being connected to the main facet by a ridge, - the applicator tip extending along the longitudinal axis, the recess extending all around the longitudinal axis of the applicator tip, - the recess forming an indentation that extends from the main facet in the direction of a proximal end of the applicator member, the thickness e of the applicator member at the indentation being between 1 mm and 5 mm, - the length D of the applicator tip being between 5 mm and 15 mm, - the applicator tip having, on its face away from the main facet, a back surface that forms the back of the applicator tip, - the applicator comprising a handle that is provided at its end with the applicator member, the handle being hollow and forming a reservoir containing the cosmetic product, the applicator member comprising, on its proximal side, a mounting end piece, the mounting end piece of the applicator member being inserted at least partially into a opening in the handle and extending at least partially into the reservoir, the handle being rectilinear, - the main facet extending along the longitudinal axis, the applicator tip extending from one end of the handle, the end of the handle extending, at its junction with the applicator tip, along a longitudinal axis, the main facet extending along the axis that forms a non-zero angle θ with the axis, and - the applicator comprising a closure cap that is attached to the handle and covers the applicator member. - the applicator member being made of a porous material that is a felt, - the main facet extending as far as the distal end, - the applicator member extending along a longitudinal axis, the main facet extending along an axis inclined at an angle α relative to the longitudinal axis, the angle α being between 0 and 45°, - the width 1 of the main facet decreasing towards the distal end of the applicator member, the maximum width lmax of the main facet being between 2 mm and 5 mm, - the longitudinal axis Z of the main facet and the recess forming an angle η of between 30° and 145° between one another at their junction, - the recess being connected to the main facet by a ridge, - the applicator tip extending along the longitudinal axis, the recess extending all around the longitudinal axis of the applicator tip, - the recess forming an indentation that extends from the main facet in the direction of a proximal end of the applicator member, the thickness e of the applicator member at the indentation being between 1 mm and 5 mm, - the length D of the applicator tip being between 5 mm and 15 mm, - the applicator tip having, on its face away from the main facet, a back surface that forms the back of the applicator tip, - the applicator comprising a handle that is provided at its end with the applicator member, the handle being hollow and forming a reservoir containing the cosmetic product, the applicator member comprising, on its proximal side, a mounting end piece, the mounting end piece of the applicator member being inserted at least partially into a opening in the handle and extending at least partially into the reservoir, the handle being rectilinear, - the main facet extending along the longitudinal axis, the applicator tip extending from one end of the handle, the end of the handle extending, at its junction with the applicator tip, along a longitudinal axis, the main facet extending along the axis that forms a non-zero angle θ with the axis, and - the applicator comprising a closure cap that is attached to the handle and covers the applicator member.