According to the pilot, after the main cabin door was closed by ramp personnel, he had a door ajar warning light on the cap panel. He reported he had flown the subject aircraft for four legs the previous day and a similar situation occurred on three of those legs, so he pulled the circuit breaker and reset it after 10 seconds. The door light was extinguished, and the pilots proceeded to takeoff. During the climb, while passing through 4000 feet above the ground, a popping sound was heard followed by a rapid decompression. The pilots noted that the main cabin door was ajar, but for safety reasons, they did not go to inspect the door. The pilots slowed the airplane to 130 knots indicated airspeed, and after landing, they noted the door had separated from the aircraft. Search efforts were made and the door was located in a field along the path of the flight. The door was flown to Scotland for further examination at Jetstream Aircraft Limited; however, the examination did not disclose evidence of mechanical malfunction.