Hörmander has presented a remarkable example of a solution of the homogeneous wave equation, which has a singularity at a running point. An analytic investigation of this solution is performed for the case of three spatial variables. The support of this solution is described, its behavior near the singular point is studied, and its local integrability is established. It is observed that the Hörmander solution is a specialization of a solution found by Bateman five decades in advance.