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Topology-transparent scheduling is suitable for highly mobile networks as it does not require recomputation of schedules when the network topology changes. It ensures bounded delay in communication and is, thus, useful for delaysensitive traffic. This paper proposes a topology-transparent scheduling scheme for a dense multi-hop packet radio network with MIMO-enabled transceivers. It employs RTS/CTS handshaking to communicate to a node how many packets it may send to its intended receiver in the ensuing data minislot. However, collision of RTS packets may lead to under-utilization of data minislots in a dense network. We devise a novel approach to mitigate this problem. In particular, we propose the use of multiple RTS minislots to handle the case where the maximum nodal degree exceeds the number of antennas in a transceiver, a situation that is not handled in the existing literature.