Yes-- and this was carried through in the Perez reboot (though it was forged by Hephaestus and not an Amazon, as in the Golden Age)
...and unbreakable means it can't be broken-- not, torn, not clipped, not cleaved-- not by DIana or anyone... SHe bound the mad War God Ares within the confines of the lasso--- pretty sure it's unbreakable...
M