1. A communication terminal connectable to a network for achieving communication via the network, comprising: a receiving control device that receives a display image and identification information transmitted from another communication terminal via the network, the display image being an image to be displayed on a display device, and the identification information being information for identifying the other communication terminal; a first display control device that displays on the display device the display image received by the receiving control device; a determining device that determines whether or not the display image is currently displayed on the display device; a first identifying device that, when the determining device determines that the display image is currently displayed on the display device, identifies a currently displayed image and the identification information of the other communication terminal that has transmitted the currently displayed image, the currently displayed image being the display image that is currently displayed on the display device; and a second display control device that, when the receiving control device receives the identification information and a predetermined image as the display image, and when the received identification information matches with the identification information identified by the first identifying device, displays at least a partial image of the received predetermined image in such a manner that the at least partial image overlaps with at least a part of a display area of the currently displayed image, or in such a manner that a display frame of the at least partial image contacts with a display frame of the display area of the currently displayed image.