  The purpose of the paper is to construct a new representation of dual
quaternions called bi$-$periodic dual Fibonacci quaternions. These quaternions
are originated as a generalization of the known quaternions in literature such
as dual Fibonacci quaternions, dual Pell quaternions and dual $k-$Fibonacci
quaternions. Furthermore, some of them have not been introduced until this
time. Then, we give generating function, Binet formula and Catalan's identity
in terms of these quaternions.
