Basaltic melt drives most of earth's volcanism. Understanding its rheology is crucial for any model of magma transport and volcanic eruption. Basaltic magma is generally treated as a quasi Newtonian liquid, but there are observations of Non-Newtonian behaviour. With a method, that allows measurement of Non-Newtonian viscosity of a representative melt (molten basaltic rock), we found a strong shear rate dependency of viscosity in a wide range of temperatures. The temperature-viscosity dependency indicates properties of the molten phase as the cause. The viscosity data are in good agreement with a power law model.