Double-edged Straight Swords

What are a few types of one-handed straight swords, preferably with two edges? You see, one of the characters in my WIP book wields a straight, double edged sword, and I don't know what that kind of sword would be called. I've tried wikipedia, but it doesn't have nearly enough swords of this sort, aside from the dao and jian. Everything else is curved, one-and-a-half, two-handed, or meant for thrusting. Thanks in advance!

Edit: Oops, I made a mistake. The dao is a single edged sword, not double edged.

Edit 2: I forgot to mention above that the sword is meant to be used with a shield.

Short sword, basket-hilted sword (not actually sure if that's one handed, but it looks one handed.)

Short swords are generally thrusting weapons, unfortunately. The thought did cross my mind to simply adapt it, but then I wouldn't have a name for the type of weapon, and proper names help me stay organized. Basket-hilt swords are definitely one handed, but are too... fancy(?) for my purposes. Sorry for not explaining this above, but I'm thinking something more knightly, that could be used with a shield. I just can't see a basket-hilted sword being used with a sword. Thanks for the reply nonetheless!