  We give an upper bound for the exponential $\sum_{m=1}^M \exp( 2i\pi f (m))$
in terms of $M$ and $\lambda$, where $\lambda$ is a small positive number which
denotes the size of the fourth derivative of the real valued function $f$. The
classical van der Corput's exponent 1/14 is improved into 1/13 by reducing the
problem to a mean square value theorem for triple exponential sums.
