The motion of the Sirius system about its center of mass causes the proper motion of the two stars across the celestial sphere to wobble, as illustrated in this animation. This can be used to detect the presence of an unseen companion.
You may illustrate this by using the buttons in the Sirius A+B animation to hide the orbits and to hide Sirius B. The corresponding motion is what we would see for Sirius A if it did not have proper motion on the celestial sphere. This motion, coupled with the proper motion of the Sirius system, gives the wobbling path noted above.
This wobble produced by an unseen companion should not be confused with the apparent wobble in the motion caused by parallax for all stars because of the Earth's motion around the Sun. This animation illustrates the effect of parallax on proper motion.