Coronal mass ejections (CMEs) are thought to be the way by which the solar corona expels accumulated magnetic helicity which is injected into the corona via several methods. DeVore (2000) suggests that a significant quantity is injected by the action of differential rotation, however Démoulin et al. (2002b), based on the study of a simple bipolar active region, show that this may not be the case. This paper studies the magnetic helicity evolution in an active region (NOAA 8100) in which the main photospheric polarities rotate around each other during five Carrington rotations. As a result of this changing orientation of the bipole, the helicity injection by differential rotation is not a monotonic function of time. Instead, it experiences a maximum and even a change of sign. In this particular active region, both differential rotation and localized shearing motions are actually depleting the coronal helicity instead of building it. During this period of five solar rotations, a high number of CMEs (35 observed, 65 estimated) erupted from the active region and the helicity carried away has been calculated, assuming that each can be modeled by a twisted flux rope. It is found that the helicity injected by differential rotation (≈ −7×1042 Mx2) into the active region cannot provide the amount of helicity ejected via CMEs, which is a factor 5 to 46 larger and of the opposite sign. Instead, it is proposed that the ejected helicity is provided by the twist in the sub-photospheric part of the magnetic flux tube forming the active region.