This paper presents a new approach to the linear scaling evaluation of density matrices in electronic structure theory. The new approach is based on the iterative computation of a special matrix function, the sign of the matrix and its performance is compared to that of some other methods developed for similar purpose. One particular variant of the sign approach turned out to be very competitive with other linear scaling density matrix evaluation algorithms, in terms of computational time and accuracy. It is also shown that a special damping technique greatly improves the stability of self-consistent field (SCF) calculations when using density matrix purification and sign methods.