One proves an analog of Glimm's lemma [Trans. Am. Math. Soc., 95, No. 2, 318-340 (1960)] by replacing the uniform norm by the trace norm ∥A∥=tr(AA^*)^1/2; if the elements of a finite type factor satisfy (up to δ) the relations which have to be satisfied by the matrix units of a finite-dimensional*-algebra A, then in their ε -neighborhoods there exist operators which satisfy exactly these relations and δ depends only on the algebraic type of A and of ε.