What was found
AFTER TAKE OFF EVERYTHING WAS GOING NORMAL UNTIL CROSSING AROUND FL370 CLIMBING FL 400, WHEN WE GOT THE CAS MESSAGE (AMBAR) CABIN ALTITUDE. INCREASING CABIN ALTITUDE UP TO 10000 FT. AT THAT TIME WE STARTED TO RUN THE CHECK LIST WHEN THE RED CABIN ALTITUDE CAS MSG APPEARED ON. AT THAT MOMENT THE CABIN ALTITUDE REACHED 13000 FT. AT THAT TIME WE REQUESTED TO MIAMI CENTER DESCENT TO FL200, THE ATC ASKED IF IT WAS CORRECT THAT ALTITUDE REQUESTED BY US, WE SAID YES WE CONFIRM. WE DID A CONTROL DESCENT DOWN TO FL200 AND THEN 15000 FT. ONCE WE BEGUN THE DESCENT WE DID THE RED CABIN ALTITUDE CHECK LIST BUT WE DIDNT GET ANY RESPONSE WHILE THE ATC ASKED US WHATS THE REASON OF OUR REQUEST, WE INFORMED ABOUT A PRESSURIZATION PROBLEM AND WE REQUEST TO RETURN TO OUR DEPARTURE AIRPORT KOPF . AT THE DESCENT THE PRESSURIZATION WAS UNDER CONTROL USING THE MANUAL MODE. THE CABIN BECAME TO DESCENT BELOW 10000 FT WITH SEVERAL VARIATION IN THE INSTRUMENT OF THE CABIN CLIMB. FINALLY WE DID A STABLE ILS APPROACH TO THE RUNWAY 09L. MIAMI CENTER ASKED ONCE IF WE REQUIRED ANY ASSISTANCE AT OUR LANDING AND WE SAID NO, WE DIDNT DECLARE THAT ISSUE AS AN EMERGENCY, THE FLIGHT WAS ALWAYS UNDER CONTROL BUT IMPOSSIBLE TO CONTINUE TO OUR INITIAL DESTINATION AIRPORTIN MEXICO (MMAN). AT THE APPROACH, WE GOT A DIRECT TO CUURT AND THEN CLEARED TO THE CUURT 1 ARRIVAL, THEN SOME VECTORS TO AVOID A FEW TRAFFICS IN THE AREA. FINALLY WE ACCOMPLISHED THE ILS TO RUNWAY 9L, WE DID A NORMAL LANDING. WE THANKED FOR ALL THE SUPPORT.