If you have knots in the end of your rope, and want to extend it right at the end, you can just use a larks head in the bight of the new rope. You can also use a larks head to extend without end knots, by collapsing it into a square-knot-like configuration. TheDuchy photos show both variations. Suspended Animation photos show only the square knot variation, with some good notes on usage.

Generally, I prefer the Sheet Bend Rope Extension because while it's slightly harder to learn, it's easier to adjust the position of the knot after tying it.