It is shown that two theorems regarding the existence of generalized linear processing orthogonal designs (GLPODs) by Tarokh, Jafarkhani, and Calderbank (in "Space-time block codes from orthogonal designs," IEEE Trans. Inform. Theory, vol. 45, pp. 1456-1467, July 1999) are valid under more general conditions than for which they have been stated and proved.