  Renz (Ann. Probab. 1996) has established a rate of convergence $1/\sqrt{n}$
in the central limit theorem for martingales with some restrictive conditions.
In the present paper a modification of the methods, developed by Bolthausen
(Ann. Probab. 1982) and Grama and Haeusler (Stochastic Process. Appl. 2000), is
applied for obtaining the same convergence rate for a class of more general
martingales. An application to linear processes is discussed.
