Kilayim, Chapter 9, Mishnah 9. The Mishnah continues to deal with methods that are not ordinary weaving, and yet still fall under the prohibition of shaatnez.
"Levadim asurim":
Levadim is the material known as felt - fibers that are not spun into threads, but rather pressed together against one another. Someone who presses flax fibers together with wool fibers transgresses the prohibition of shaatnez, even though he did not spin them into threads and did not use any of the other ordinary methods of making fabric. And the reason is: "mipnei shehem shu'im" - because one process was performed on them, the combing and brushing of the fibers, and once this process has been done they are forbidden as shaatnez.
The Rishonim disagree as to whether the very act of combing and combining creates a Torah-level prohibition of shaatnez, or whether it is only a rabbinic prohibition. Either way, all agree that it is forbidden.
"Hapif shel tzemer beshel pishtan assur":
A "pif" is a border, and the case is a wool border placed on a linen garment. The reason it is forbidden: "mipnei shehen chozrin ba'arig" - the border surrounds the garment and is surrounded by it, and so its status is as though the wool and the linen were woven together, and they may not be with one another.
The words of Rabbi Yosi:
Rabbi Yosi says: "meshichot shel argaman asurot" - cords made of argaman, which is wool dyed purple, may not be used on a linen garment, to serve as a sort of belt for the linen garment. And his reason: "mipnei shehu molel ad shelo kosher" - it was the practice to sew, and "molel" means to sew the cord onto the linen garment in order to make use of it. This is generally the case with belts, that they are normally sewn, and one usually sews the belt before tying it to hold the garment in place.
"Lo yikshor seret shel tzemer beshel pishtan, lachgor bo et matnav":
In a similar case of a belt, the Mishnah rules that one may not tie a wool strap together with a linen strap in order to gird his loins with them. And even in a case where "haretzuah ba'emtza" - where a leather strap separates between the two - it is still forbidden, for although the wool and the linen are not lying alongside one another, in the end the person ties them together into a belt in front of him.
In summary: In this Mishnah we learned that the prohibition of shaatnez is not limited to weaving alone: felt is forbidden because of the "shu'im" process done to it, a wool border on a linen garment is forbidden because it comes back around into the weave, and according to Rabbi Yosi even argaman cords are forbidden because of the sewing that precedes the tying. And even a leather strap separating between a wool ribbon and a linen ribbon does not permit it, since in the end the two are tied together into a single belt.