Supersonic head-on collisions between quiescent clouds produce flattened sheets of shocked gas. We derive the condition which the cooling law must satisfy if this sheet is to fragment into protostellar condensations (i.e. gravitationally unstable lumps). If this condition is not satisfied, colliding clouds are likely to be disrupted and dispersed. We show that under the conditions obtaining in GMCs, most cloud-cloud collisions probably do not result in fragmentation.