A tangent device of a sewing machine of the invention comprises a stationary knife and a movable knife which are installed on the lower surface of a needle plate installed in front of a soleplate, and facial sutures and bottom lines are cut by reciprocating rotation of the movable knife. A driving source enables a second connecting bar to move back and forth installed inside the soleplate. The second connecting bar is connected with a connecting part installed at the upriver side of the driving transmission path and opposite to the needle plate. The connecting part is connected with the first connecting bar enabling the movable knife to rotate, and transmits the fore-and-aft movement of the second connecting bar to the first connecting bar, so that the movable knife carries out reciprocating rotation. An adjusting mechanism for adjusting the position of the movable knife is installed on the connecting part. The adjusting mechanism does not include a component overlapped with the movable knife and the stationary knife. Worn-out movable knives or stationary knives can be easily replaced in a short time in the condition of not breaking down the adjustable mechanism.