A reclosable container for consumer items includes a box, a lid hingedly connected to the box, an inner liner wrapped around the consumer items, the inner liner including a section defining an opening for allowing access to the consumer items, means to open and reclose the opening, and an inner frame attached to the box. The inner frame includes a free inner frame portion protruding from the box towards the opening in the inner liner. The free inner frame portion includes a cut out and the inner frame is attached to the inner liner proximate to the cut out.