We determined the change in orientation of the electronic transition dipole moment with respect to the membrane normal in the K, L, and M intermediates of bacteriorhodopsin using transient linear dichroism. Purple membranes were oriented in a 14 T magnetic field and immobilized in a gel. The oriented purple membranes were excited isotropically and the transient absorbance changes were detected with the sample between two parallel polarizers. The absorbance changes were measured as a function of wavelength, time, and angle between the orientation axis and polarizer direction. In this way, the transient changes in isotropic absorbance, linear dichroism, and linear birefringence were determined with high accuracy. The Kramers-Kronig transform of the transient linear dichroism was in excellent agreement with the transient linear birefringence and this served as a useful control on the reliability of the linear dichroism data. We developed a novel formalism to extract the anisotropies, spectra and time courses of the photocycle intermediates in a model-independent way from the combined analysis of the transient absorbance and linear dichroism data. Whereas an analysis based on transient absorbance data alone is underdetermined, we show that in combination with transient linear dichroism data a unique solution may be obtained for the early intermediates K, L, and M. The analysis makes use of the constraints that (1) the sum of the populations of the K, L, and M intermediates is constant in time and (2) the absorption for the M intermediate vanishes for lambda greater than or equal to 520 nm. For wild-type bR at pH 7 (10 degrees C) we obtained in this way the following wavelength-independent anisotropies for the main absorption band: r(bR) = -0.145, r(K) = -0.140, r(L) = -0.132, and r(M) = -0.139. Similar experiments were carried out for the mutant D96A which allows more accurate experiments for the L and M intermediates under various conditions of temperature and pH (pH 7, 20 degrees C; pH 4.7, 20 degrees C; pH 4.7, 10 degrees C). In all cases there are very clear differences in the anisotropies and the sequence is always r(bR) < r(K) < r(M) < r(L). The data analysis is validated by the fact that the spectra and time courses of the intermediates are in excellent agreement with previous work. Making the reasonable assumption that the order parameter characterizing the orientational distribution is the same for each intermediate, the anisotropy changes translate into small orientational changes for the transition dipole moment: Delta theta(K) = -0.8 + 0.2 degrees, Delta theta(L) = -1.7 +/- 0.2 degrees, Delta theta(M) = -1.1 +/- 0.3 degrees. The largest change occurs in the L intermediate. The angle with respect to the membrane normal is smaller in every intermediate than in the ground state. The simplest interpretation of the results is that after the isomerization of the C-13-C-14 double bond the C-5-N direction remains approximately the same with the C-5-C-13 part of the polyene chain tilting out of the plane of the membrane.