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With the progress in nanoscale thermoelectric materials and devices the need for accurate characterization of these structures has become more apparent. Among the main three thermoelectric material properties of electrical conductivity, Seebeck coefficient, and thermal conductivity accurate measurement of thermal conductivity seems to be the most challenging due to its strong sensitivity to parasitic heat transfer paths. In this report we present a method for accurate measurement of the thermal conductivity of a thermoelectric nanowire structure. The method takes into account the heat loss to the substrate and the supporting materials which are the main parasitic heat conduction paths. The method can be extended to measure the thermal conductivity of other thermoelectric structures such as superlattice thin films and nanoparticles.