  Using cluster tilting theory, we investigate tilting objects in the stable
category of vector bundles on a weighted projective line of weight type $(2, 2,
2, 2)$. More precisely, a tilting object consisting of rank-two bundles is
constructed via cluster tilting mutation. Moreover, the cluster tilting
approach also provides a new method to classify the endomorphism algebras of
tilting objects in the category of coherent sheaves and the associated bounded
derived category.
