The waveform interpolation is one of the speech coding algorithms with high quality at low bit rates. In the WI coding, the vector quantization of SEW requires a variable dimension quantization technique since the dimension of the SEW amplitude spectrum varies depending on the pitch period. However, since the variable dimension vector makes a difficulty to employ conventional vector quantization techniques directly, some dimension conversion techniques are usually utilized for the quantization of the variable dimension vectors. In this paper, we propose a new dimension conversion method for the SEW quantization in order to reduce the cost of codebook storage space with a small conversion error in the wideband WI speech coding. This dimension conversion method would be more useful for the wideband speech because wideband speech requires larger codebook memory for the variable dimension vector quantization compared to narrowband speech.