The relation between MS and logM0 is examined using Harvard CMT M0, with both and the improved surface wave magnitude scale [1] applied to ISC data. Although shows less scatter than , neither dataset supports a slope of MS against logM0 which tends to 1.0 towards smaller magnitudes. Instead, a good linear fit of slope 0.76 using is found throughout the fitted range of M0 (2.0×1024 to 1.26×1027 dyne-cm), and this linearity extends down to M0=2.5×1023 dyne-cm. This suggests that previous proposals that MS data support a theoretical slope of 1.0 in the low range of magnitude which may be expected from established relationships, is not justified.