  The geometric measure of entanglement of a pure quantum state is defined to
be its distance to the space of product (seperable) states. Given an
$n$-partite system composed of subsystems of dimensions $d_1,\ldots, d_n$, an
upper bound for maximally allowable entanglement is derived in terms of
geometric measure of entanglement. This upper bound is characterized
exclusively by the dimensions $d_1,\ldots, d_n$ of composite subsystems.
Numerous examples demonstrate that the upper bound appears to be reasonably
tight.
