In this article we describe a new technique for measuring the thermal conductivity of dielectric films a few hundred nanometres thick supported by substrates. The method utilizes a 0.6-mu-m wide, 500-mu-m long metal line for-med on the surface of the film to be tested. The metal line serves as a heat source and as a sensor of its own temperature increase. Measurement is made in about 1-mu-s and this completely eliminates any possible substrate effects on the conductivity results. The feasibility of the method has been initially confirmed by measurements made on bulk fused quartz. Silicon dioxide (SiO2) films (0.1-1-mu-m thick), produced on silicon substrates by thermal oxidation, have thermal conductivities between 1.35 and 1.55 W m-1 K-1, which is almost identical to that of bulk fused quartz. The accuracy of these measurements is estimated to be better than +/- 10%.