An exercise machine for exercising muscles in the back of an exerciser, includes: a frame; a seat assembly attached to the frame; a movement arm pivotally attached to the frame and movable along a stroke path between an upper forward position and a lower rearward position; a resistance-imparting unit operatively connected with the movement arm to provide resistance to the movement arm as it moves from the forward position to the rearward position; a pair of handles to be grasped by the exerciser; and a pair of extension members, each of which is attached to a respective handle such that each handle is free to rotate about a longitudinal axis of the extension member. The extension members are attached to the movement arm such that each extension member is free to at least partially rotate relative to the movement arm about vertical, longitudinal and transverse axes. Also, the extension members are of sufficient length and the extension members are attached to the movement arm (preferably via universal ball joints) so that the handles can be separated by a distance of at least 24 inches when the movement arm is in the rearward position. In this configuration, the exerciser has the option of performing the basic lat pulldown motion with the hands in any orientation, and can pull the handles to multiple positions in front of the chest and shoulders or outside the chest and shoulders.