What do you call a katana without the hand guard?

I'm sure it's koshigatana (waist sword). It's a sword shorter than katana.

Katana Without Guard

It all depends on the mounting, really. I'll give you my thoughts on what it could be.

Aikuchi - A mount type where there is no tsuba (handguard) to speak of. The metal fuchi (reinforcement ring on the tsuka/handle closest to the blade) meets the koiguchi (opening of the sheath). It's a fairly sleek style found mostly on tanto, but I have seen it on katana and wakizashi size examples on occasion.

Hamidashi - A mount type with a very small, rounded tsuba that is only slightly larger around than the saya and tsuka. Most often found on shoto (tanto and wakizashi), but again, I have seen some examples on full length katana.

Shikomizue - Japanese stick sword. Many of these were made to look like branches turned into walking sticks, some were made to look like canes, others were made to look like staffs. They were always disguised as something else besides a sword.

Shirasaya - Plain wood storage fittings. This is a mount not intended for combat. It is made of un-lacquered or un-painted wood. They can be octagon or rounded in shape, and will never have any metal fittings. They are always a plain, natural wood finish. This type of mount is only for storage, to allow the sword to breathe and not trap any moisture inside like lacquered wood might.

well, the katana is a japanesse sword right. if it haven't a hand guard, can be that the grip of the katana is make with wood. but if the katana have an hand guard, is a traditional katana.

the person that answer it up of my answer, says that is a shorter katana. a shorter katana is called nitog kodachi

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It depends on how the sword was constructed. Look at the handle for 1 or 2 small bamboo pins. If you see these, they can be removed, and the sword disassembled. If no pins are visible, check the very end of the handle for a bolt (check google for 'rat tail tang'.