A construction method for insulating a building exterior. The method includes fixing an L-shaped anchor provided with a vertical portion and a horizontal portion on a building exterior wall, fixing a bracket, and fixing a plurality of lightweight stone insulating panels. The bracket includes a horizontal support portion, an upward fixing portion bent upward from the horizontal support portion, a downward fixing portion bent downward from the horizontal support portion, and an extending support portion extending forward from the horizontal support portion to the L-shaped anchor. The lightweight stone insulating panels includes an insulating board, a stone plate attached to a front surface of the insulating board, and a reinforcing board attached to a rear surface of the insulating board to the building exterior wall. The stone plate is supported by the extending support portion.