A new streamline method for the solution of convection-dominated transport problems is introduced. First, an analysis is made of the nature of classic streamline upwinding from the perspective of space and spacetime solution domains, as they pertain to the nature of the problems. From this analysis emerges a rigorous logic for upwinding, which can easily be implemented in the full (spacetime) Galerkin formulation of the transport equation. Comparative performance testing of this technique, in solving a number of examples, proves it to be robust and versatile. The advantage of this method resides in its applicability to a wider range of Courant numbers.