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We present the properties of the first 250 μm blind sample of nearby galaxies (15 < D < 46 Mpc) containing 42 objects from the Herschel Astrophysical Terahertz Large Area Survey. Herschel's sensitivity probes the faint end of the dust luminosity function for the first time, spanning a range of stellar mass (7.4 < M⋆ < 11.3 log10 M⊙), star formation activity (-11.8 < SSFR < -8.9 log10 yr-1), gas fraction (3-96 per cent), and colour (0.6 < FUV-KS < 7.0 mag). The median cold dust temperature is 14.6 K, colder than in the Herschel Reference Survey (18.5 K) and Planck Early Release Compact Source Catalogue (17.7 K). The mean dust-to-stellar mass ratio in our sample is higher than these surveys by factors of 3.7 and 1.8, with a dust mass volume density of (3.7 ± 0.7) × 105 M⊙ Mpc-3. Counter-intuitively, we find that the more dust rich a galaxy, the lower its UV attenuation. Over half of our dust-selected sample are very blue in FUV-KS colour, with irregular and/or highly flocculent morphology; these galaxies account for only 6 per cent of the sample's stellar mass but contain over 35 per cent of the dust mass. They are the most actively star-forming galaxies in the sample, with the highest gas fractions and lowest UV attenuation. They also appear to be in an early stage of converting their gas into stars, providing valuable insights into the chemical evolution of young galaxies. [ABSTRACT FROM AUTHOR]