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Jaroslav Folda of the University of North Carolina described the gonfalons of several military orders as follows:
The Templar battle standard is well known to have been a long narrow vertical rectangle, argent with a chief sable, that is a white standard topped by a broad band of black. This is the famous gonfalon baucent, or the piebald standard. We know about this standard from the Rule of the Templars. The Hospitaller standard was a white cross on a red field, and the standard of the Teutonic knights was a black cross on a white field. As is well known, these banners or standards were specifically represented as such by Matthew Paris in the mid-thirteenth century along with many other heraldic devices.
Matthew Paris' depiction of the banner appears in the Chronica Maiora, Parker MS 16 fol. 141r, dated to c. 1250, and the Historia Anglorum, Royal MS 14 C VII, fol. 130v.
In Chronica Maiora, the Hospitaller gonfalon is shown alongside the banner of the Templars and the Oriflamme of France:
While in the Historia Anglorum it is shown with just the banner of the Templars:
Notice that in this case, both banners are inverted. This is not uncommon with depictions in marginalia.