  We consider products of matrices of the form $A_n=O_n+\epsilon N_n$ where
$O_n$ is a sequence of $d\times d$ orthogonal matrices and $N_n$ has
independent standard normal entries and the $(N_n)$ are mutually independent.
We study the Lyapunov exponents of the cocycle as a function of $\epsilon$,
giving an exact expression for the $j$th Lyapunov exponent in terms of the
Gram-Schmidt orthogonalization of $I+\epsilon N$. Further, we study the
asymptotics of these exponents, showing that
$\lambda_j=(d-2j)\epsilon^2/2+O(\epsilon^4|\log\epsilon|^4)$.
