An algorithm is applied here to compute folding pathways of staphylococcal protein A, fragment B. Emphasis is on studies of the complete process, starting from an ensemble of fully denatured conformations and ending at the folded state. The stochastic difference equation algorithm is based on optimization of an action that makes it possible to use a large integration step. Motions with typical displacements that change rapidly on the size scale of the step are filtered out, providing numerically stable and approximate solutions. The present approach is unique in maintaining an atomically detailed picture while providing a systematic, controlled approximation to the classical equations of motion. Analysis of 130 trajectories suggests the following folding mechanism for protein A: At an early precollapse phase of the process, a few native hydrogen bonds form near the C terminus of the protein. The hydrogen bonds are formed mostly within the third helix. The next step is chain collapse that occurs in parallel to additional growth of secondary structure seeds. Therefore, the present study does not support a pure hydrophobic collapse, or substantial early formation of secondary structure. At the last step, native tertiary contacts are formed at the same time as the completion of the secondary structure elements. To a large extent, the process is parallel and not sequential. The early formation of the third helix of protein A, fragment B (in the calculation), is consistent with experimental data.