The Polarization and Directionality of Earth Reflectances (POLDER) instrument was routinely functioning aboard the second Advanced Earth Observing Satellite (ADEOS-2) from April to October 2003. A series of algorithms dedicated to Earth radiation budget, water vapor, and clouds are applied to the POLDER data. This paper presents the derivation scheme of the narrowband albedos at the top of the atmosphere from POLDER measurements at 443, 670, and 865 nm. These narrowband albedos are used to estimate the broadband shortwave albedo at the top of atmosphere in a companion paper. Here we focus on the 670 nm (over land)/865 nm (over ocean) albedo. Although our derivation is based on the plane-parallel hypothesis, and thanks to the multidirectional capability of POLDER, results appear reliable for both cloudy and clear-sky scenes. A quality index is introduced from the comparison between the angular variability of the retrieved "directional" albedo values and that of the measured reflectances. This quality index is "good" in 80% of the cases. Moreover, the retrieved albedo values are found to be statistically little dependent on the viewing direction.