In this letter, a novel Golden-Hadamard codebook (GHC) scheme is proposed to improve the performance of the traditional precoded Alamouti coding for multiple-input and single-output systems. Although the traditional discrete Fourier transform codebook (DFTC) performs satisfactorily with Alamouti coding and offers numerous benefits for the Rayleigh fading channel, this scheme inherently generates huge codeword distortion, which leads to a lower minimum chordal distance (MCD). Furthermore, the uncertain format of all prior versions of codebooks results in poorer minimum determinant (MD) values. Hence, the proposed GHC scheme successfully deals with the issues of traditional DFTC to achieve a better codebook format that completely overcome both MCD and MD problems. The effectiveness of the proposed GHC scheme is confirmed, in terms of bit-error-rate through Monte Carlo simulations.