IEEE 802.16j Mobile Multihop Relay specification is an amendment of the IEEE 802.16 standard and it is developed to extend IEEE 802.16e. Quality of Service (QoS) constrained service flow management is an important issue related to these networks. In the situation where the link quality between a superordinate station and one of its subordinate Non-Transparent Relay Stations (NTRSs) is poor then it is difficult to fulfill the QoS requirements of the flows that are passing through that NTRS. To handle such situations, in this paper, a novel Cooperative Data Transmission (CDT) framework is proposed. It uses the Transparent Relay Stations (TRSs) which are the common neighbors of the NTRSs and their superordinate stations to fulfill the QoS requirements of the flows that are passing through the NTRSs. The changes required to the network entry, path establishment, bandwidth allocation and data transmission processes of the IEEE 802.16j standard for the CDT framework are proposed in this paper. Also, the performance gains achievable with the proposed CDT framework in terms of the throughput are analyzed numerically. The upper and lower bounds on the throughput gain are obtained. Through simulations, the performance of the proposed CDT framework is studied and compared with the performance of the normal data transmission where no cooperation from TRSs is involved in the data transmission. The CDT framework showed significant performance advantages when compared with the normal data transmission method.