We present a new algorithm for tangent height retrievals from limb-scattering observations. These observations are performed by satellite-based spectrometers operating in the UV, visible, and short-wave IR spectral ranges. They record the solar radiation scattered in Earth's atmosphere in limb-viewing geometry and aim at vertically resolved retrievals of the atmospheric composition with global coverage. Inaccuracies in the knowledge of the instrument's pointing frequently dominate the error budgets of the atmospheric composition products. Therefore, additional information on satellite pointing is crucial for the quality of all products derived from limb-scattering observations. The information is commonly expressed in terms of the tangent heights. The presented algorithm determines the tangent heights directly from the observed limb radiances by analyzing the shapes of the so-called knee in several UV-B radiance profiles. All vertical pointing information contained in a UV-B fit window is exploited by simultaneously retrieving the ozone profile. The algorithm has been implemented in the toolbox SCIARAYS and named Tangent height Retrieval by UV-B Exploitation (TRUE) knee method. We have applied it to five orbits of SCIAMACHY's limb observations. It achieves a precision of about 200 m when applied to an individual limb scan. The broadband structure of the observations can be reproduced within 1% RMS. A comparison of the retrieved tangent heights with the engineering ones delivered by ESA reveals that the engineering tangent heights exhibit a systematic error, which varies with an amplitude of about 3 km. Its origin is traced to the on-board orbit model of Envisat. PACS Nos.: 94.80.+g, 42.68.Ay, 92.60.Ta, 42.68.Wt, 07.87.+v, 92.70.Cp, and 07.60.Rd