  We propose a mechanism for the spontaneous (gauge-invariant) reduction of
noncommutative ${\cal U}(n)$ gauge theories down to SU(n). This can be achieved
through the condensation of composite ${\cal U}(n)$ gauge invariant fields that
involves half-infinite Wilson lines in trace-U(1) noninvariant and SU(n)
preserving direction. Based on this mechanism we discuss anomaly-free fully
gauge invariant noncommutative Standard Model based on the minimal gauge group
${\cal U}(3)\times {\cal U}(2)\times {\cal U}(1)$, previously proposed, and
show how it can be consistently reduced to the Standard Model with the usual
particle spectrum. Charge quantization for quarks and leptons naturally follows
from the model.
