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We measure the heights of EUV bright points (BPs) above the solar surface by applying a stereoscopic method to the data taken by the Solar TErrestrial RElations Observatory/SECCHI/Extreme UltraViolet Imager (EUVI). We have developed a three-dimensional reconstruction method for point-like features such as BPs using the simple principle that the position of a point in the three-dimensional space is specified as the intersection of two lines of sight. From a set of data consisting of EUVI 171 Å, 195 Å, 284 Å, and 304 Å images taken on 11 days arbitrarily selected during a period of 14 months, we have identified and analyzed 210 individual BPs that were visible on all four passband images and smaller than 30 Mm. The BPs seen in the 304 Å images have an average height of 4.4 Mm, and are often associated with the legs of coronal loops. In the 171 Å, 195 Å, and 284 Å images the BPs appear loop-shaped, and have average heights of 5.1, 6.7, and 6.1 Mm, respectively. Moreover, there is a tendency that overlying loops are filled with hotter plasmas. The average heights of BPs in 171 Å, 195 Å, and 284 Å passbands are roughly twice the corresponding average lengths. Our results support the notion that an EUV BP represents a system of small loops with temperature stratification like flaring loops, being consistent with the magnetic reconnection origin.