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Reef Knot
A "Reef Knot" is basically a Standard Shoelace Knot minus the loops. This is useful when the ends are not long enough to tie a regular bow, such as when a shoelace has broken and there is no ready replacement. Also known as a "Square Knot".
Step 1:
Reef Knot diagram 1
Tie a Left-over-Right Starting Knot as shown. Note the short ends, which would make it difficult to create the loops needed to tie a Standard Shoelace Knot.
Step 2:
Reef Knot diagram 2
The steps for tying are the exact opposite of the Starting Knot. Cross the right (blue) end over the left (yellow) end. The right (blue) end is now on the left side.
Step 3:
Reef Knot diagram 3
Begin to wrap the left (blue) end around the front of the right (yellow) lace to end up at the back of the gap between the laces.
Step 4:
Reef Knot diagram 4
Feed the left (blue) end through the gap to emerge at the front left hand side. Pull tight to complete the knot.

Finished Knot
Finished Reef Knot picture The finished Reef Knot with two very short ends. It would be nearly impossible to make such short ends into long enough loops to tie a Standard Shoelace Knot.

Technical Details
Military Usage:
I've been told that the Reef Knot has been used by those in the U.S. Army, with the ends simply tucked into the top of the boots, the theory being that there are then no loops that could snag and come undone.
Untying the Reef Knot:
Most shoelace knots are untied by simply pulling on either or both of the ends. These act as "drawstrings", which pull the loops back through the knot until it falls apart.

Because the Reef Knot has neither loops nor drawstrings, many people resort to picking it apart. However, it can also be undone as follows:
Step 1:
Reef Knot diagram 5
Pull either end straight upwards until its curves have been pulled into a straight line. In this example, the right (yellow) end has been pulled straight.
Step 2:
Reef Knot diagram 6
The left (blue) end is still wrapped around the right (yellow) end with a double-loop. Simply slide this double-loop up and outwards along the straight (yellow) lace until it falls off the end.

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Related Links
Standard Knot Standard Knot
Regular shoelace knot done with loops, which requires more length.
User-controllable Reef Knot animation Flip Book
User-controllable animation of the Reef Knot sequence.
The 'Granny Knot' The "Granny Knot"
Explains why a balanced "Reef Knot" stays secure whereas an un-balanced "Granny Knot" comes undone.

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