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Although René Girard has been given a second life in literary criticism, the contributions of his “mimetic system”, together with his analysis of the “sacrificial crisis”, have been too quickly forgotten in the theological field. There are a number of reasons for this oversight. However, this does not mean that we should avoid making use of a number of interesting ideas formulated by René Girard. Indeed, one must now dare to go beyond the Girardian model. Within the limits of this article the author indicates fairly formal guidelines for this new exploration by using matrix calculation. This will lead him to complement Girard’s thought by taking seriously both human sin and the grace of a living God.