An algorithm for updating the evidence in the Dempster-Shafer theory is presented. The algorithm is based on an idea of indices. These indices are used to code the process of reasoning under uncertainty (the combination of evidence)using the Dempster-Shafer theory. The algorithm allows to carry out the reasoning with updating the evidence in much more efficient way than using the original Dempster-Shafer theory. Updating the evidence is necessary among others in systems that are based on changing data – adaptive and distributed reasoning systems.