A method for the local initial application of a thermal barrier coating layer (3), or for the local repair of coating defects and/or deteriorations of components (1) in the hot gas path of a gas turbine engine, which components are coated with a thermal barrier coating layer, includes at least the following steps: (I) in the case of repair, normally overall inspection of the whole component (1) for the determination of the location of defect/deterioration, as well as of corresponding type of defect/deterioration of each place for a multitude of locations of the component (1); (II) if needed, preparation of the surface in at least one location; (III) local application of a ceramic tissue together with a wet chemical thermal barrier coating layer deposition material for the formation of a patch (5) of ceramic matrix composite; (IV)a intermediate inspection of the patch and/or the surface; (IV)b in the case of a repetitive and/or multi-step repair method, subsequent layer application of a ceramic tissue together with a wet chemical thermal barrier coating layer deposition material for the formation of a patch (5) of ceramic matrix composite at this location; (V) if needed, surface finishing at the at least one location; and (VI) final inspection of the at least one location. Steps (IV)a, (V) and (VI) can be omitted with the provision that at least one of steps (IV)a or (VI) is carried out.