The extracellular giant hemoglobin from the earthworm Lumbricus terrestris was reconstructed at 14.9-Angstrom resolution from cryo-electron microscope images, using a new procedure for estimating parameters of the contrast transfer (CTF) function. In this approach, two important CTF parameters, defocus and amplitude contrast ratio, can be refined iteratively within the framework of 3D projection alignment procedure, using minimization of sign disagreement between theoretical CTF and cross-resolution curves. The 3D cryo-EM map is in overall good agreement with the recent X-ray crystallography map of Royer et al (2000, Proc. Natl Acad. Sci. USA 97,7107-7111), and it reveals the local threefold arrangement of the three linker chains present within each 1/12 of the complex. The 144 globin chains and 36 linker chains within the complex are clearly visible, and the interdigitation of the 12 coiled-coil helical spokes forming the central toroidal piece is confirmed. Based on these findings, two mechanisms of the dodecameric unit assembly are proposed and termed "zigzag" and "pairwise" polymerizations. However, the detection by cryo-EM of 12 additional rod-like bodies within the toroid raises the possibility that the architecture of the toroid is more complex than previously thought or that yet unknown ligands or allosteric effectors for this oxygen carrier are present.