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Arrays of microtriodes have recently become available due to the development of microfabricated field-emission electron sources. Computer simulation has shown that the brightness of beams emitted by them is significantly higher than that of the common microbeams, and possible application of the accelerated beam to free electron lasers has been discussed. Experimentation on beam generation has started, but methods for diagnosing the beam have not yet been established. Difficulty is predicted, because of the high brightness, in applying the conventional methods of emittance measurement. In this paper we propose a new method that determines the emittance without using apertures. The cross section of a converging beam is elongated by a quadrupole lens, and parameters of the emittance ellipse are obtained from the beam size on a screen when changing either the strength or the axial position of the quadrupole lens.