  H. W. Lenstra \cite{lenstra} introduced the notion of an Euclidean ideal
class, which is a generalization of norm-Euclidean ideals in number fields.
Later, families of number fields of small degree were obtained with an
Euclidean ideal class (for instance, in \cite{hester1} and \cite{cathy}). In
this paper, we construct certain new families of biquadratic number fields
having a non-principal Euclidean ideal class and this extends the previously
known families given by H. Graves \cite{hester1} and C. Hsu \cite{cathy}.
