The construction and operation of a new fully automated microcalorimeter is described.This instrument allows specific heat measurements to be performed on small samples in the 10 mg-range at low temperatures (10 K <T < 350 K). The new method consists of ombining the non-adiabatic relaxation-time calorimetry with a twin arrangement and simultaneous temperature scanning. Some experimental details of the calorimeter and sample holders are presented. The accuracy of the calorimeter was verified by calibration measurements on 56 mg of copper. An energy resolution of 0.1μJ/K has been reached near 12 K. To demonstrate the reliability of the microcalorimeter the heat capacity of the new highTc superconductor YBa2Cu3O7−y, was determined.