1. A video encoding method for encoding a video image by dividing an entire image into areas, generating a predicted image for each area of the divided image based on image information of a plurality of already-encoded frames, and encoding differential information between an image of an encoding target area in an encoding target frame and the predicted image, the video encoding method comprising: a reference vector target frame selecting step of selecting a reference vector target frame indicated by a reference vector of the encoding target area, from among the already-encoded frames; a matching step of selecting a reference frame from among the already-encoded frames, and setting a reference vector target area which belongs to the reference vector target frame and has the same size as the encoding target area, in a manner such that an error in matching between image information of the encoding target area and image information of a reference area in the reference frame is minimized, where the image information of the reference area corresponds to image information of the reference vector target area due to block matching; a predicted reference vector generating step of generating a predicted reference vector as a predicted vector of the reference vector of the encoding target area, by using the reference vector target frame of the encoding target area and a reference vector and a reference vector target frame which are used when encoding an adjacent area of the encoding target area; a reference vector target frame designation information encoding step of encoding information which designates the reference vector target frame of the encoding target area; a differential reference vector encoding step of encoding a differential vector between the reference vector and the predicted reference vector of the encoded target area; a reference frame designation information encoding step of encoding information which designates the reference frame; a predicted image generating step of generating the predicted image by using the image information of the reference area in the reference frame; and a differential information encoding step of encoding differential information between the image information of the encoding target area and the generated predicted image, wherein: the reference frame selected in the matching step is one of a reference frame and a reference vector target frame, which was used when encoding the reference vector target area, where: when said one of a reference frame and a reference vector target frame is a reference frame, the reference area in the reference frame is a reference area which was used when encoding the reference vector target area, and when said one of a reference frame and a reference vector target frame is a reference vector target frame, the reference area in the reference frame is a reference vector target area which was used when encoding the reference vector target area; and each of the steps are performed by a computer processor.