Abstract: In this study, the idea of unitary operator of Pauli matrices is employed in a new algorithm. One of the most attractive properties of this algorithm is that, we can decide when to change the operations of the algorithm whenever it is statistically necessary. The underlying operations in this algorithm are unitary operators of Pauli matrices which can be represented by using rotation matrices. The researcher divided the combination of the Pauli matrices into three groups where we perform the operation (II, σ_x , σ_y and σ_z ) in each group. Using developed encryption algorithm could encrypt the message, being transmitted over an insecure channel. The keys are created using a BB84 protocol where we require two keys K₀ K₁ to encrypt a qubit and this is important in order to hide all information in all possible bases the qubit could be in. The security analysis and an example illustrating how the algorithm works are presented in this study. An overview of the complete process from the generation of the algorithm to the decryption of the message is illustrated explicitly.