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A study of the magnetic field penetration depth in a high-temperature (HT c ) superconducting film was performed with polarized neutron reflectometry in two scattering geometries. The fit to the reflectivity curves yielded the neutron-scattering length density profile and thus a precise image of the composition of the film. The film had a good quality seen by a not noticeable off-specular scattering. The fit to the spin asymmetry gave a magnetic-penetration depth of 1350 +/- 150 9 along the c-axis at a temperature T = 2 K. The model included an intrinsic exponential decay of the penetration depth. For the first time the spin asymmetry was determined with high resolution over an extended Q-range for a HT c -film.