Ballistic missiles are used to deliver nuclear, chemical, biological or conventional warheads in a ballistic flight trajectory. On the other hand, an anti-ballistic missile (ABM) is generally a surface-to-air missile designed to counter ballistic missile. So, it is clear that to make the operation or mission of an inter-continental ballistic missile (ICBM) successful we have to eliminate the threat of anti-ballistic missile (ABM). This paper will discuss about the arrangement of a small tracking system and some small missiles attached with the main ballistic missile which can destroy any anti-ballistic missile (ABM) coming towards it. So, simply this small air-to-air missiles act as anti-missiles for any incoming anti-ballistic missile (ABM) which is targeting the main ballistic missile and we can simply call them anti-anti-ballistic missiles (AABM).