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The Brewster's law predicts zero reflection of p-polarization on a dielectric surface at a particular angle. However, when loss is introduced into the permittivity of the dielectric, the Brewster condition breaks down and reflection unavoidably appears. In this work, we found an exception to this long-standing dilemma by creating a class of nonmagnetic anisotropic metamaterials, where anomalous Brewster effects with independently tunable absorption and refraction emerge. This loss-independent Brewster effect is bestowed by the extra degrees of freedoms introduced by anisotropy and strictly protected by the reciprocity principle. The bandwidth can cover an extremely wide spectrum from dc to optical frequencies. Two examples of reflectionless Brewster absorbers with different Brewster angles are both demonstrated to achieve large absorbance in a wide spectrum via microwave experiments. Our work extends the scope of Brewster effect to the horizon of nonmagnetic absorptive materials, which promises an unprecedented wide bandwidth for reflectionless absorption with high efficiency.