Multicasting is a spectrally efficient method of supporting group communication by allowing transmission of packets to multiple destinations using fewer resources. To incorporate Multi-Input Multi-Output diversity, Extended Balanced Space-Time Block Codes (EBSTBCs) have been proposed providing full diversity when one or more feedback bits are sent back via feedback channel. However, the EBSTBCs are designed for unicast communication in the literature. This paper presents a novel wireless multicasting scheme which selects the optimum EBSTBC for all mobile users to support wireless multicast. Extensive, detailed simulations are performed to show the feasibility of full rate and full diversity multicast service provisioning in Rayleigh fading channels.