Let A ∈ Rn×n and let B ∈ Rn×p and consider the Lyapunov matrix equation AX + XAT + BBT = 0. If A + AT < 0, then the extended Krylov subspacemethod (EKSM) can be used to compute a sequence of low rank approximations of X. In this paper we show how to construct a symmetric negative definite matrix A and a column vector B, for which the EKSM generates a predetermined residual curve.