B737 Undifferentiated or Other Model
Flight Crew Air Transport Pilot (ATP)
Aircraft Equipment Problem Critical
Flight Crew Returned To Departure Airport
Aircraft
We were climbing from ZZZ enroute to ZZZ1.  Climbing past approximately FL320 (32;000 feet); we heard the cabin altitude warning horn with the associated warning light.  The three of us immediately donned our oxygen masks.  As the non-flying pilot; I completed the associated quick action items according to the QRH (Quick Reference Handbook).  The cabin pressure was leaking and was not controllable.  It was not a rapid decompression; but it was steadily rising above 10;000 feet cabin altitude.  We got an immediate clearance from ATC (Air Traffic Control) to descend and return to ZZZZ.  The remainder of the QRH items were completed and we landed at ZZZZ normally.  There was no other indication as to why we had a depressurization.  All door lights were extinguished; there was no abnormal system warning of any kind; etc.Perhaps this aircraft could use some extra scrutiny in the hangar by the maintenance department.  I know it is a high time/cycle aircraft.
B737 Captain reported a cabin depressurization during climb and decided to return to the departure airport.