We present a new technique based on the method developed by Metz and Fencil for estimation of the 3D imaging geometry and 3D object configurations from biplane angiographic acquisitions. The new method employs the 3D configuration of points calculated by the Metz-Fencil technique as an initial estimate. A 3D Procrustes algorithm is employed to translate, rotate, and scale the configuration until it aligns optimally with the set of lines that connects a focal spot with the corresponding set of image points. This alignment procedure is applied independently for each view. The rotation and translation that relate the two aligned data sets are then determined by an additional 3D Procrustes calculation. These steps are applied iteratively. Evaluations were based on Monte Carlo simulation and phantom studies. With this new technique, the mean absolute errors in magnification, in the relative position of the points, and in the angles defining the rotation and translation matrices were approximately 3.0%, 1.5 mm, and 5 degrees and 3 degrees, respectively, for rms input errors in the image data up to 2.0 pixels (0.7 mm). Errors in the results can be as small as 0.5%, 0.16 mm, 0.6 degrees, and 0.3 degrees, respectively, if input image-data error is 0.035 mm. The improvement of the Metz-Fencil technique described here may provide a basis for precise estimation of the biplane imaging geometry and the 3D positions of vessel bifurcation points.