Website no longer active but pattern can still be found through the internet archive.

From Pattern Notes:

A Möbius strip is a continuous, one-sided surface formed by twisting one end of a rectangular strip through 180° about the longitudinal axis of the strip and attaching this end to the other. When this concept is applied to knitting, it makes a useful scarf that, because of the half-twist, will lie flat under a coat. The Moebius (American spelling) scarf can be pulled over the head loosely or twisted into a figure 8 and brought over the head for a snug fitting head and neck scarf. The concept of knitting a lace Mobius Scarf in the first place was originated by Elizabeth Zimmermann and first published in 1983. The design was then published in Elizabeth’s fourth book, Knitting Around and has appeared in Knitter’s magazine. This is my version.