In this note, we present the solution to the algebraic Riccati equation (ARE) with indefinite sign quadratic term related to the H-infinity control problem for singularly perturbed system by means of a Kleinman's type algorithm. The resulting algorithm is very efficient from the numerical point of view because the ARE is solvable even if the quadratic term has an indefinite sign. Moreover, the resulting iterative algorithm is quadratically convergent. We also present a new algorithm for solving the generalized algebraic Lyapunov equation (GALE) on the basis of the fixed point algorithm.