A subsea clamp connector for connecting the ends of two tubular members to each other, the clamp connector including first and second clamping elements, which are pivotable into a closed position in clamping engagement with the ends of the tubular members; and a replaceable locking unit for locking the clamping elements in the closed position. The locking unit includes an operating shaft, a first retaining member mounted to the operating shaft and configured for engagement with a shoulder on a holding member fixed to the first clamping element, and a second retaining member mounted to the operating shaft and configured for engagement with a shoulder on a holding member fixed to the second clamping element. The locking unit is detachably mountable to the clamping elements by insertion of the operating shaft sideways into slots provided in the holding members.