A polybenzoxazole (PBO) membrane from a self-cross-linked aromatic polyimide polymer membrane is provided. These membranes are useful in the separation of gas mixtures. The PBO membrane is made by fabricating a self-cross-linkable aromatic polyimide polymer membrane comprising both hydroxyl functional groups and carboxylic acid functional groups; cross-linking the polymer to form a self-cross-linked aromatic polyimide polymer membrane by heating the membrane at 250° to 300° C. under an inert atmosphere; and thermal heating the self-cross-linked aromatic polyimide polymer membrane at a temperature from about 350° to 500° C. under an inert atmosphere to convert the self-cross-linked aromatic polyimide polymer membrane into a PBO membrane. A membrane coating step may be added by coating the selective layer surface of the PBO membrane with a thin layer of high permeability material.