  We simulate 50 off-lattice DLA clusters, one million particles each. The
probability distribution of the angle of attachment of arriving particles with
respect to the local radial direction is obtained numerically. For increasing
cluster size, $N$, the distribution crosses over extremely accurately to a
cosine, whose amplitude decreases towards zero as a power-law in $N$. From this
viewpoint, asymptotically large DLA clusters are locally $isotropic$. This
contradicts previous conclusions drawn from density-density correlation
measurements [P. Meakin, and T. Viscek, Phys. Rev. A {\bf 32}, 685 (1985)]. We
present an intuitive phenomenological model random process for our numerical
findings.
