In situ synchrotron powder X-ray diffraction measurements have demonstrated that SrUO4 undergoes a reversible phase transformation under reducing conditions at high temperatures, associated with the ordering of oxygen defects resulting in a lowering of crystallographic symmetry. When substoichiometric rhombohedral alpha-SrUO4-x, in space group R (3) over barm with disordered in-plane oxygen defects, is heated above 200 degrees C in a hydrogen atmosphere it undergoes a first order phase transformation to a (disordered) triclinic polymorph, delta-SrUO4-x, in space group P (1) over bar. Continued heating to above 450 degrees C results in the appearance of superlattice reflections, due to oxygen-vacancy ordering forming an ordered structure delta-SrUO4-x. Cooling delta-SrUO4-x toward room temperature results in the reformation of the rhombohedral phase alpha-SrUO4-x with disordered defects, confirming the reversibility of the transformation. This suggests that the transformation, resulting from oxygen vacancy ordering, is not a consequence of sample reduction or decomposition, but rather represents a change in the energetics of the system. A strong reducing atmosphere is required to generate a critical amount of oxygen defects in alpha-SrUO4-x to enable the transformation to delta-SrUO4-x but once formed the transformation between these two phases can be induced by thermal cycling. The structure of delta-SrUO4-x at 1000 degrees C was determined using symmetry representation analysis, with the additional reflections indexed to a commensurate distortion vector k = (1/4 1/4 3/4). The ordered 2D layered triclinic structure of delta-SrUO4-x can be considered a structural distortion of the disordered 2D layered rhombohedral alpha-SrUO4-x structure through the preferential rearrangement of the in-plane oxygen vacancies. Ab initio calculations using density functional theory with self-consistently derived Hubbard U parameter support the assigned ordered defect superstructure model. Entropy changes associated with the temperature dependent short-range ordering of the reduced U species are believed to be important and these are discussed with respect to the results of the ab initio calculations.