  Lenstra introduced the notion of a Euclidean ideal class, which is a
generalization of the Euclidean domain. Lenstra also proved that the Euclidean
ideal in a number field $K$ implies that the class group of $K$ is cyclic. We
construct a family of biquadratic fields with a Euclidean ideal whenever the
class number is 2. This extends the families given by Graves, Hsu,
Chattopadhyay, and Muthukrishnan.
