I have made many two-part menko in the past year —probably a couple of thousand— and have come up with a more efficient method of producing them. I am passing on what I have learned in case you wish to make a garland of two-part menko to decorate your tree.
Pre-folding all the parts for a large number of two-part menko can lead to pairs that don’t fit together, especially if you are mixing different sorts of paper. The method below makes one menko at a time and the two parts always fit. (If you get incredibly bored with making menko, this method also means you never have a bunch of left-over, un-assembled parts.)
The model was made with moderately heavy wrapping paper cut 2.5 cm/1 in wide. The weight and stiffness of your paper will determine the maximum width that is workable.
Cut two strips of paper to a suitable width and as long as possible. (I have cut the length of my strips in half for the photographs.) Fold the bottom left corner of each strip up to the top edge to form a triangle.
Fold the left end over on each strip, matching the top of the triangle to the upper edge of the strip below.
Lay one strip horizontally. Lay the second trip at right angles to the first, then slide the second strip into the first, with the flat part under the triangle of the first strip and the second strip’s triangle on top.
Fold the horizontal strip to the left, over the two triangles, and cut off the long end. Your cut should be in line with the left edge of the lower strip.
Unfold the cut end, then fold the top right corner down to form a triangle.
Fold the newest triangle to the left over the previous triangles and fold the bottom strip up over the whole unit. Cut the strip horizontally to match the upper edge of the unit.
Unfold the newly-cut end, then fold the bottom right corner of the newly cut edge up to form a triangle.
Tuck the tip of the bottom triangle under the lower edge of the left hand triangle.
You can try using a long needle to thread the menko together for a garland, but I found it was quicker to open each one and lay the thread in.
Undo two triangles of your menko and lay your thread across. (My thread is high-twist mercerized crochet cotton, which is very strong.)
Lift a third triangle and slip the thread under it.
Fold and tuck to re-close your menko.
If you are planning to use your garland to decorate a room rather than a tree, and will have long unsupported stretches, you might want to stabilize your garland every few feet. You can do this by taping the thread in place before closing the menko. (If you want the garland to be passed down for generations to come, use a bit of paper and some starch paste to do the job.)