The Collaborative International Dictionary of English v.0.48:

Cordonnet \Cor`don`net"\ (k?r`d?n`n?"), n. [F., dim. of cordon.
   See Cardon.]
   Doubled and twisted thread, made of coarse silk, and used for
   tassels, fringes, etc. --McElrath.
   [1913 Webster]