To provide a repair-reinforcement processing method with respect to a slate building material containing an asbestos fiber component.

A composite covering material 10, having a metal thin plate 12 stuck on one surface of a heat insulating plate member 11 and including an overlapped splicing means 13 along an overlapped splicing direction, is prepared. A construction part is moistened and is cleaned by a vacuum cleaner with a HEPA filter and a water-circulation type cleaner. The composite covering materials are overlappingly spliced with a metal thin plate surface directed outward via the overlapped splicing means, waterproofing means 24 are laid at overlapped splicing parts of respective composite covering materials, and the composite covering materials are installed on an outer surface of a slate roof, or the like. At a position of a ridge part of a slate where a beam means is located, the composite covering materials are fixed to a slate outer surface by fitting/fixing means 17 via a means for preventing scattering of chips or the like. An air passage means 25 is arranged, at the rear surface side of the laid composite covering material, and an air-flow adjusting function for keeping cool air in summer by releasing heated air on a roof and warm air in winter by suppressing the flow of air is arranged.