The paper discusses an analogue of Householder's similarity transformations, which reduces a full pseudo-symmetric matrix to a tridiagonal pseudo-symmetric matrix. A pseudo-symmetric matrix $A$ is defined by $A=BJ$ when $B=B^T$ and $J$ is a diagonal matrix with diagonal elements plus or minus unity. Due to the form of these transformations the term coresponding to $S^2$ in Householder's method can be negative and admit complex value of $S$. A simple modification of the method allows the use of only real arithmetic.