A combustor of a gas turbine, comprising a transition piece and a combustor air plenum, the transition piece comprising: an impingement cooling zone, which is provided with impingement cooling holes 201, an impingement cooling arrangement having a sidewall of a sequential liner and an impingement plate attached to the sidewall of the impingement cooling zone and a chamber between the impingement plate and the sidewall, a sequential disposed liner having at least one cooling arrangement, a closing plate with respect to the sequential disposed liner, the sequential disposed liner having a cooling channel structure, wherein the cooling channel structure forms a closed loop cooling scheme or a quasi-closed loop cooling scheme, and wherein the cooling channel structure is operatively connected to a cooling medium to cool at least one part of the sequential disposed liner, wherein the cooling channel structure comprises: cooling channels extending through the thickness of the sequential disposed liner of the transition piece, and an annular space (407, 408) on a side of the closing plate, wherein the cooling channels comprise first cooling channels having first openings to the combustor air plenum and second cooling channels having second openings to a space inside the chamber, wherein the cooling channels, which run in a serpentine manner, are actively connected to the annular space (407, 408) and redistribute the cooling medium among one another, wherein the cooling channels are applied in the wall of the sequential disposed liner in one or more circumferentially subsequently disposed section, and wherein the cooling channels have suitable cross-sectional size. an impingement cooling zone, which is provided with impingement cooling holes 201, an impingement cooling arrangement having a sidewall of a sequential liner and an impingement plate attached to the sidewall of the impingement cooling zone and a chamber between the impingement plate and the sidewall, a sequential disposed liner having at least one cooling arrangement, a closing plate with respect to the sequential disposed liner, the sequential disposed liner having a cooling channel structure, wherein the cooling channel structure forms a closed loop cooling scheme or a quasi-closed loop cooling scheme, and wherein the cooling channel structure is operatively connected to a cooling medium to cool at least one part of the sequential disposed liner, wherein the cooling channel structure comprises: cooling channels extending through the thickness of the sequential disposed liner of the transition piece, and an annular space (407, 408) on a side of the closing plate, cooling channels extending through the thickness of the sequential disposed liner of the transition piece, and an annular space (407, 408) on a side of the closing plate, wherein the cooling channels comprise first cooling channels having first openings to the combustor air plenum and second cooling channels having second openings to a space inside the chamber, wherein the cooling channels, which run in a serpentine manner, are actively connected to the annular space (407, 408) and redistribute the cooling medium among one another, wherein the cooling channels are applied in the wall of the sequential disposed liner in one or more circumferentially subsequently disposed section, and wherein the cooling channels have suitable cross-sectional size.