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An existing UCS can be rotated by a specified angle. The origin of the system remains unchanged, only the direction of UCS’s axes changes accordingly. The rotation is performed in the adjusted working plane, i.e. the axis of rotation is normal to the current working plane.
If it is not the case that the UCS you want to move is the active one, make it active first.
Make sure that the working plane is adjusted properly, i.e. that it is oriented in such a way that a normal to the working plane is parallel with the axis of intended rotation.
Call menu function Tools > UCS > Rotate (You may as well activate toolbar function Setting of UCS for active view> Rotate from toolbar View).
Type the angle by which the UCS should be rotated.
Close the dialogue.
Note: Please read Rules for using a UCS.