In this paper, a novel closed‐loop multiple antennas transmission scheme suitable for M = 2p(p ⩾2) transmit antennas is proposed on the basis of the extended orthogonal space–time block codes. And, all 2p transmit antennas are divided into p groups, and each group includes two antennas, and Alamouti orthogonal space‐time block code is adopted. All p groups are used to transmit the same source symbols, and each group is scaled by one scale matrix before transmission. The elegantly designed scale matrix takes both power allocation and phase rotation into account to optimise the antenna array gain and exploit full transmit diversity while maintaining low linear decoding complexity provided by Alamouti code. By formulating the problem as a convex optimisation problem, the optimal solution for the scale matrix is achieved. In addition, several practical feedback codebook design methods are proposed, and their advantages over the existing closed‐loop extended orthogonal space–time block code schemes are clearly demonstrated by both analysis and simulation results. Copyright © 2012 John Wiley & Sons, Ltd.