Marginal reliability importance (MRI*) of a component in a system is defined as the rate at which the system reliability changes over changes of the component reliability. MRI helps network designers to construct a reliable network layout. We consider a problem to compute MRI of all components in a network system considering all-terminal reliability in order to rank the components with respect to MRI. The problem is time-consuming since computing network reliability is #P-complete. This paper improves the traditional approach for the problem to proposes an efficient algorithm. The algorithm applies some network transformations, three network reductions and one network decomposition. We have proved lemmas with respect to the relationship between the transformations and MRI, which compute MRI for an original network by using MRI and reliability for transformed networks. Additionally, we have derived a deformed formula to compute MRI, which can also reduce computational task. Numerical experiments revealed that the proposed algorithm reduced computational time considerably compared to the traditional approach.