C500 DIVERTS WHEN DOOR UNLOCKED LIGHT ILLUMINATES. DOOR NOT PROPERLY LATCHED.

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WE DEPARTED ZZZ1. THE SKY WAS CLR AT THE TIME. ALL ANNUNCIATORS WERE INDICATING NORMAL WHEN WE DID THE FINAL FLAPS; ANNUNCIATORS; TRIMS; SPD CHK BEFORE TKOF. APCH CTL GAVE US A VECTOR; CLRNC TO CLB TO 13000 FT; AND HANDED US OFF TO CENTER. CLBING THROUGH APPROX 5000 FT THE DOOR UNLOCKED LIGHT CAME ON. WE LEFT THE FASTEN SEATBELT LIGHT ON AND THE SIC TRIED TO VISUALLY CHK THE DOOR FROM THE R SEAT. HE WAS UNABLE TO VERIFY ANYTHING FROM HIS SEAT. I PUT THE AIRPLANE ON AUTOPLT; PASSED CTL TO THE SIC; AND QUICKLY LEFT MY SEAT TO CHK THE DOOR VISUALLY. I SAW RIGHT AWAY THAT THE WHITE LINES ON THE LATCHING MECHANISM WERE MISALIGNED; INDICATING THAT THE DOOR WAS NOT PROPERLY LATCHED. I ADVISED THE PAX THAT WE WOULD BE LNDG AT ZZZ2 AND TO KEEP THEIR SEATBELTS FASTENED; RETURNED TO MY SEAT; TOOK ACFT CTL AND DIRECTED THE SIC TO RUN THE ABNORMAL CHKLIST FOR THE DOOR UNLOCKED LIGHT. I LEVELED THE PLANE AT 11000 FT AND INFORMED CENTER THAT WE NEEDED TO LAND AT ZZZ2 TO CHK OUT THE DOOR. WE WERE RIGHT OVER ZZZ2 AT THE TIME AND I AM FAMILIAR WITH THE ARPT. CENTER CLRED US DIRECT TO ZZZ2 AND HANDED US BACK TO APCH. WE MADE A NORMAL LNDG AT ZZZ2; PULLED ONTO THE TXWY AND SET THE BRAKE. I THEN WENT BACK TO THE DOOR; LATCHED IT PROPERLY; SAW NOTHING ABNORMAL ABOUT THE DOOR; AND THE SIC CHKED THAT THE DOOR UNLOCKED LIGHT WAS OUT. WE DEPARTED ZZZ2 AND COMPLETED THE TRIP UNEVENTFULLY. WITH THE CITATION 500 SERIES DOOR; IT IS CRITICAL TO NOT GO OVER CTR WHEN PUTTING THE DOOR HANDLE IN THE LOCK POS. I HAVE ALWAYS DEMONSTRATED TO NEW SIC'S WHAT CAN HAPPEN IN THAT CASE. THE DOOR PINS ARE NOT LATCHED! I WAS PLANNING THIS FOR THE LAYOVER; BUT SHOULD HAVE DONE IT SOONER.