The Off-hand black sword is a black sword equipped in the offhand slot. It can be obtained as a drop from various monsters, or by trading with another player. It can also be found in chests that require Steel keys in the Shades of Mort'ton minigame.
For an exhaustive list of all known sources for this item, see here.
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Trivia
Before an update on 17 June2013, all off-hand black equipment, with the exception of claws, was unobtainable and could only be seen by searching for it on the Grand Exchange.