The present invention is a two stage PSA process for producing high purity oxygen from a feed air stream. Water, carbon dioxide and nitrogen are removed in a first stage. An oxygen selective adsorbent is used to adsorb oxygen in the second stage. High purity oxygen product is recovered during regeneration of the second stage. Importantly, the high purity of the oxygen product is achieved without inclusion of an oxygen rinse step in the process cycle. The high purity oxygen product is obtained by collecting the middle cut of the second stage effluent stream during regeneration.