The main objective of the research is to specify two dimensional passwords that can possess much more strength as compared to linear passwords. These passwords are strong enough to provide effective and secure authentication under certain alarming situations. The alarming situations are the situations where the possibility to breach the system security exists. The specification of the two dimensional nxn passwords has been provided based on NIST standards. The strength of nxn password has been calculated that has proven to be much more as compared to the linear passwords. It is proposed that these passwords should be used under alarming situations such as the protection requirement for some critical resource, special authentication when the system is in unsafe state or protection of sensitive data. Therefore it has been recommended to move from linear passwords to the passwords defined in two dimensional space, whenever some alarming situation arises. © 2010 IEEE.