A connecting system is provided for detachably connecting a first pipe end to a second pipe end. The first pipe end has a sealing cone facing toward the second pipe end and a shoulder section. The connecting system includes a first clamping disk surrounding the first pipe end and a second clamping disk surrounding and connected to the second pipe end. The connecting system further includes a multiplicity of screws, detachably connecting the first clamping disk to the second clamping disk. The first clamping disk includes an outer circular disk ring and an inner circular disk ring which is detachably connected to the outer circular disk ring. The inner circular disk ring has multiple separate circular disk ring parts, and an outer diameter of the inner circular disk ring is greater than an outside diameter of the shoulder section provided on the first pipe end.