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The Collaborative International Dictionary
Counterflory

Counterflory \Coun"ter*flo`ry\ (-fl?`r?), a. [See Counterfleury.] (Her.) Adorned with flowers (usually fleurs-de-lis) so divided that the tops appear on one side and the bottoms on the others; -- said of any ordinary.

Wiktionary
counterflory

a. (context heraldry English) Decorated with fleur-de-lis or other floral motifs arranged in pairs opposite each other, especially on opposite sides of a border on a shield or banner.