THE AIRLINE TRANSPORT PILOT-IN-COMMAND AND COMMERCIAL PILOT PASSENGER DEPARTED KENDALL-TAMIAMI EXECUTIVE AIRPORT, MIAMI, FLORIDA, ON A VFR PERSONAL FLIGHT. VFR CONDITIONS PREVAILED AND NO FLIGHT PLAN WAS FILED. A WITNESS OBSERVED THE AIRPLANE TRAVELING WESTBOUND AT ABOUT 200 FEET AGL. THE AIRPLANE WAS OBSERVED TO CONDUCT AN UNCOORDINATED AILERON ROLL TO THE RIGHT. UPON COMPLETION OF THE AILERON ROLL, THE AIRPLANE WAS OBSERVED TO CONDUCT AN ABRUPT PITCH UP MANEUVER, SHAKE VIOLENTLY AND DESCENDED TAIL LOW. AN INCREASE IN ENGINE POWER WAS HEARD, THE AIRPLANE STARTED A RIGHT TURN, THE NOSE OF THE AIRPLANE DROPPED TO A NOSE DOWN ATTITUDE, AND THE AIRPLANE DISAPPEARED BELOW THE TREE LINE. ANOTHER WITNESS STATED HE HEARD A 'POP-POP' SOUND FOLLOWED BY A LARGE BANG. THE WITNESS LOOKED UP AND SAW THE AIRPLANE TRAVELING EASTBOUND SPINNING TO THE RIGHT IN A NOSE DOWN ATTITUDE. A SEPARATE LARGE PART WAS OBSERVED DESCENDING TO THE GROUND AS THE AIRPLANE DISAPPEARED FROM VIEW BELOW THE TREE LINE. THE AIRPLANE WAS DESTROYED. THE AIRLINE TRANSPORT PIC, AND COMMERCIAL PILOT PASSENGER WERE FATALLY INJURED.