LASO2 - FORTRAN implementation of the Lanczos process with selective orthogonalization. The LASO package is a set of FORTRAN IV subroutines for computing a few eigenvalues of a large (sparse) symmetric matrix. The LASO package is documented in a technical report [3]. This article documents the changes to the LASO package which were incorporated into LASO2. The primary difference between LASO and LASO2 is that LASO2 does not use EISPACK to compute the eigenvalues of the band matrix generated by the Lanczos algorithm. It also monitors all the eigenvalues of interest at every Lanczos step rather than selected ones. Other changes were incorporated at the same time and are described in this article. The user guides for the two entry points for LASO2 (subroutines SNLASO and SILASO) are given at the end. These guides are virtually identical to the user guides for the old LASO package. In particular, the calling sequences for SNLASO and SILASO are the same for both versions.