This paper presents how the space of spheres and shelling may be used to delete a point from a d-dimensional triangu- lation efficiently. In dimension two, if k is the degree of the deleted vertex, the complexity is O( k log k), but we notice that this number only applies to low cost operations, while time consuming computations are only done a linear number of times. This algorithm may be viewed as a variation of Heller’s algorithm [He190, Mid93], which is popular in the geographic information system community. Unfortunately, Heller algorithm is false, as explained in this paper.