A larger version (6 yard length of rope) of Walking Knot won the FISM award in 1982. This same effect is now availble in the 6 foot version here and can be performed everywhere and under close-up conditions.
The magician displays a length of rope and cuts it into two parts of 14" and 60". the two pieces are tied together. Suddenly the knot slowly moves from it's end towards the middle of the rope which is held outstretched between the magician's hands. The knot slides to the center and the magician unties it showing that the rope is cut at this new position!
The effect is immediately repeated. The rope is retied in the middle and held between the hands of the magician again. The knot moves slowly towards the opposite end of the rope and is untied there!
In the end, the rope is retied and then magically restored with the knot having vanished!
You get the rope and complete instructions for performance and handling.
As a bonus, you also get Krazy Knot.
Here a knot is tied in the middle of a piece of rope. Then another knot is tied, and another, and so on until almost the whole rope is used up and a large ball of knots is in the center of the rope. Finally while holding an end of the rope in each hand, the performer blows on the ball of knots. Instantly the ball of knots detaches itself from the rope and falls to the floor! The performer remains with a short length of rope between his hands.