This problems solves Laplaces equation on a sphere of radius 1 with the Boundary Element Method (BEM). The sphere has 4 elements in the circumfrential direction and 4 elements in the azimuthal direction. The basis functions are cubic Hermite (including sector elements). The value of the dependent variable at each of the nodes is set according to x^2-y^2.The numerical results are compared to the known analytic formula for this problem.