In addition to the backstrap loom two other kinds of looms are used in Bhutan: the frame loom and the card loom.
Frame looms do not use a circular warp like the backstrap loom, and were introduced from Tibet in the first half of the 20th century. Fabric produced is limited to a narrower width than on the backstrap loom: a full kira woven on a backstrap loom will be made of 3 pieces of fabric oriented horizontally, but a full kira woven on a frame loom will need around a dozen pieces oriented vertically (see Tibetan Hothra, for example).
A card loom is set up on a backstrap loom frame using a circular warp and is used for weaving very narrow pieces, such as belts. Each card has 4 holes, and each card has a group of 4 warp threads threaded through the 4 different holes in such a way that as the set of cards is rotated 90 degrees or 180 degrees between each row, a new shed is formed.
The cards are only tied together like this when no-one is weaving.
For more about Bhutanese card weaving, see Claire Ozel’s informative article Tablet Weaving in Bhutan