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A free-wave, transmission only technique for the determination of complex permittivity in the millimetre (mm)-wave band 14-40 GHz of planar samples of textiles is presented. With this method an accurate alignment of source and detector horns is not required and time gating methods to reduce or remove standing wave interference between horns is replaced by a data smoothing process. The technique is novel as phase information from the transmitted wave is not required to determine the complex permittivity. The textiles investigated are denim (cotton) and cow leather (two colours, red and beige). This method is shown to be simple to set up, easy to use and fast when compared with other methods such as free-wave reflectance and transmittance or Fabry-Perot cavity and gives results which are accurate enough for most of the practical applications. A significant difference in the absorption of mm-wave power between the two leather samples is observed. This can be explained by the different chemical composition of the two leather samples, investigated using a scanning electron microscope with electron dispersive spectrometry and which is almost certainly a result of the colouring process employed.