This paper extends the results of Hojgaard and Taksar (1997a) to the case of posititve transactions costs. The setting here and in HCjgaard and Taksar (1997a) is the following: When applying a proportional reinsurance policy rr the reserve of the insurance company {R~ r } is governed by a SDE dR~ -----(/z -(1 -aT(t)))~dt + aT(t)~r dWt, where {Wt} is a standard Brownian motion,/z, a > 0 are constants and ~. > #. The stochastic process {aT(t)} satisfying 0 < aT(t) _< 1 is the control process, where 1 -aT (t) denotes the fraction of all incoming claims, that is reinsured at time t. The aim of this paper is to find a policy that maximizes the return function VT(x) = ~_fo ~ e-CtR~ dr, where c > 0, rx is the time of ruin and x refers to the initial reserve. In Hcjgaard and Taksar (1997a) a closed form solution is found in case of ~. = /x by means of Stochastic Control Theory. In this paper we generalize this method to the more general case where we find that if ~. >__ 2/z, the optimal policy is not to reinsure, and if/z < ~. < 2p., the optimal fraction of reinsurance as a function of the current reserve monotonically increases from 2(~. -#)/)~ to 1 on (0, xl) for some constant xj determined by exogenous parameters.