We demonstrate that the phenomenon of extraordinary optical transmission (EOT) through perforated metal films can be further boosted up by utilizing nanofocusing of radiation in tapered slits. For one-dimensional arrays of tapered slits in optically thick suspended gold films, we show that the maximum transmission at resonance is achieved for taper angles in the range of 7-10 degrees increasing significantly in comparison with the transmission by straight slits. Transmission spectroscopy of fabricated 500 and 700 nm period tapered slits in a 180 nm thick gold film on a glass substrate demonstrates the enhanced EOT with the resonance transmission being as high as approximately 0.18 for the filling ratio of approximately 0.13 and showing good correspondence with theoretical results. It is also shown that the enhanced transmission can be achieved with either weak (2.5%) or strong (43%) reflection depending on the direction of light (normal) incidence.