  In 1983, N. Herrndorf proved that for a $\phi$-mixing sequence satisfying the
central limit theorem and $\liminf_{n\to\infty}\frac{\sigma^2_n}n>0$, the weak
invariance principle takes place. The question whether for strictly stationary
sequences with finite second moments and a weaker type ($\alpha$, $\beta$,
$\rho$) of mixing the central limit theorem implies the weak invariance
principle remained open.
  We construct a strictly stationary $\beta$-mixing sequence with finite
moments of any order and linear variance for which the central limit theorem
takes place but not the weak invariance principle.
