The present work aims at studying a new concept of a vertical tailless aircraft provided with a morphing tail solution with the purpose of eliminating the drag and weight created by the vertical tail structure. The solution consists on a rotary horizontal tail with independent left and right halves to serve as control surfaces. Different static scenarios are studied for different tail configurations. The proposed morphing configurations are analyzed in terms of static and dynamic stability and compared with a conventional configuration. The stability derivatives defining the limits of static stability are calculated for the whole range of tail rotation angles. The aircraft’s dynamic model is developed and feedback control systems are implemented. A sideslip suppression system, a heading control system and a speed and altitude hold system are studied for three different configurations, MC1, MC2 and MC3 configurations. Static results show that the aircraft is longitudinally stable for a wide range of tail rotation angles. Variation of tail dihedral and rotation angles are two mechanisms able to maintain directional and lateral stability but only the last is able to produce lateral force and yawing moment. Dynamic stability results demonstrate no spiral nor Dutch-roll modes due to the absence of the vertical stabilizer. The increase in tail rotation produces an appearance of the spiral mode and an unstable Dutch-roll mode that quickly degenerates into two unstable real roots with the increase in tail rotation. The addition of dihedral to the tail increases the stability of the overall modes while decreasing their variation amplitude with the tail rotation. The morphing tail configuration proved to be a feasible control solution to implement in an aircraft such as a small UAV, with the MC1 configuration being the most simple of the three morphing configurations and also the most reliable one.