A frame connecting member of a kite formed as a unitary body and of an elastic material comprises a main body whose front and rear ends are formed as projections provided with kite string mounting holes and whose center is formed as a base with a through hole in the longitudinal direction for a longitudinal frame member; and supports provided respectively at the right and left outer sides of the base on the same straight line in the direction which perpendicularly intersects the axis of the main body. The supports can be tilted to a certain angle with respect to the straight line and are provided with holes into which are inserted lateral frame members which perpendicularly intersect the through holes. The corners on the main body side of the supports come in contact with the main body so as to prevent any further tilting. The kite string mounting holes are directed in the same direction as that of the through hole of the base.