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

On the existence of a non-principal Euclidean ideal class in biquadratic fields with class number two