Composite delamination represents one of the most critical failure mechanisms occurring in composite structures. In case complex structures are being designed, numerical methods need to be employed. One of the methods to numerically simulate delamination in a Finite Element environment is through the employment of the Cohesive Elements, which embed the theory constituting the Cohesive Zone Model. Nonetheless, the computational time required to assess delamination simulations by implementing the Cohesive Elements is restrictive, because the presence of a strong stress gradient at the crack tip imposes the adoption of a small-size mesh at the same location. In this context, a sensible improvement is deemed to be necessary, such as to promote these methodologies from an instrument used in academia to an effective solution. A novel type of Cohesive Element is here proposed, aiming to loosen the compelling requirement on the mesh size and, by extension, to reduce the computational time required to achieve numerical simulation of composite delamination. The High Oder CE has been validated through comparison with benchmark solutions of delamination processes occurring in Mode I, Mode II and Mixed Mode opening.