  A recently proposed definition of a linear connection in non-commutative
geometry, based on a generalized permutation, is used to construct linear
connections on GL_q(n). Restrictions on the generalized permutation arising
from the stability of linear connections under involution are discussed.
Candidates for generalized permutation on GL_q(n) are found. It is shown that,
for a given generalized permutation, there exists one and only one associated
linear connection. Properties of the linear connection are discussed, in
particular its bicovariance, torsion and commutative limit.
