In this paper, Orthogonal Space Time Block Coding (OSTBC) is combined with linear precoding matrices to improve the exploitation of the different diversities for a multicarrier transmission. The linear precoding matrices based on Hadamard construction are proposed where a simple linear de-precoder can be chosen at the receiver part which performs closely to the Maximum Likelihood (ML) global precoded OSTBC decoder. The system is generalized to different numbers of transmit antennas and different sizes of precoding matrices. Performance results have been obtained in theoretical and real channel environments. It is shown that the combined scheme efficiently exploits the space, time and frequency diversities while using a linear decoder. This system leads to an OSTBC with maximal diversity for more than two antennas when a Zero Forcing (ZF) or a Minimum Mean Square Error (MMSE) equalizer is chosen.