Unlike quaternions and split quaternions, reduced biquaternions satisfy the multiplication commutative rule and are commonly used in image processing, fuzzy recognition, image compression, Hopfield neural networks, and digital signal processing. However, although algebraic techniques have been developed for the diagonalisation of quaternion and split quaternion matrices, the diagonalisation of a reduced biquaternion matrix is yet to be studied. In this study, we derive sufficient and necessary conditions for the diagonalisation of a reduced biquaternion matrix and devise two numerical methods for the diagonalisation of a reduced biquaternion matrix. These methods were derived using complex and real representations in the reduced biquaternionic algebra.