Also called “The Afgan Bands” and “The Red Muslin Bands”. In effect, a band of paper or cloth is torn in half along its circumference, but instead of yielding two separate bands, produces two linked bands or one large band. The method relies on the topological properties of the Möbius strip, formally documented by August Ferdinand Möbius and Johann Benedict Listing in 1858. The principle, transformed into the trick we know, entered formal conjuring literature in the anonymous Art of Modern Conjuring, 1885, p. 134.

By the late 1800s, French professional magician Félicien Trewey had added the trick to his act, greatly popularizing it. P. T. Selbit (Percy Thomas Tibbles) coined the lasting name of the trick when he called it “The Mystic Afghan Bands” in his Magician's Handbook, 1901, p. 62. Selbit explains the name: “This trick is supposed to have been invented and worked by the old Indian fakirs[….] Whether or not that is true I do not know […]” It turns out it wasn't. There is no supporting evidence of an East Indian origin for the trick.

In the first decades of its use by magicians, the Afghan Bands was performed with paper strips, which were cut with scissors. Finding this process time consuming in a professional performance, Carl Brema began to use strips of muslin, which could be quickly torn in half. Brema is given credit for this idea by James C. Wobensmith in The Magic World, Vol. 7 No. 5, Sep. 1923, p. 68. In the same article, Wobensmith describes his variant for preparing the cloth strip, which was earlier marketed by Brema, with credit to Wobensmith, in the January 1922 issue of The Sphinx, Vol. 20 No. 11, p. 415. Wobensmith, in his 1923 article, says he developed his version “some time ago”. It may have been a shorter period, if Martin Gardner is correct in dating Brema's adoption of muslin c. 1920 (see Gardner's Mathematics, Magic and Mystery, 1956, p. 71). Wobensmith's preparation has become the long-standing preferred method.