A new framework within which an integrable defect may be described is introduced in the classical context (type II defect). It relays on the introduction of a new degree of freedom located on the defect and coupled to the discontinuity of the fields across the defect. Its features will be analyzed and few concrete examples will be provided. In particular, this new scheme allows to provide a description of the Tzitzeica model with a defect, which was not possible in the previous approach (type I defect).