In this paper, we explore the use of the multi-frame GMM-based block quantiser for quantising line spectral frequencies for wideband speech coding. Its main advantages over vector quantisers are bitrate scalability and bitrate independent complexity. By concatenating multiple frames together, interframe correlation can be exploited by the KLT, leading to better quantisation. A saving of up to 3 bits/frame can be achieved by switching the quantiser from memoryless mode to jointly quantising two frames, with only a moderate increase in complexity. This quantisation scheme achieves lower spectral distortion than the split-multistage vector quantiser in the AMR-WB speech codec, with transparent coding at 37 bits/frame.