The classical problem of driving a time-invariant linear systemdx/dt = Ax + Bufrom the initial statex(t0)to the final statex(t1)is reconsidered. A method is developed to find a control vectoru(t)which drives the system fromx(t0)tox(t1)along the time-trajectoryx =exp(At )p+ exp(Ft)q, whereF, pandqare constant matrices. The method has the advantage that one can avoid computation of integrals invoking matrix functions ; if a solution exists,u(t)=B(1)(F — A)exp(Ft)q, whereB(1)is any {l}-inverse of B.