New conversion coefficients from air kerma free-in-air, Ka, to directional dose equivalent at 0.07mm depth, H'(0.07), are provided for monoenergetic values and for the spectra of the radiation qualities defined in ISO 4037-1. The interpolation procedure of the monoenergetic conversion coefficients from ICRU Report 57 was improved compared to former publications. The values resulting from the new interpolation procedure describe the energy dependence of the conversion coefficients more accurately and differ by up to 5% between 50keV and 100keV from former values. Due to an additional change of the extrapolation to low energies, the values for angles of radiation incidence above 60° and energies below 40keV changed by up to 50%. The influence on the spectrum weighted conversion coefficients is similar to the changes of the monoenergetic values.