Closely following the results of Lamberton, Pham, and Schweizer [5] we construct a locally risk-minimizing strategy in a general incomplete market including transactiou costs. This is done in dbcrete time under the assurnptious of a bounded meanvariance tracleoff and substantial risk. Once we establbh all the required integrability conditions, a backward induction argument is implemented to obtain the desired strategy for every square-integrable contingent claim. \Ve model the trnusactiou costs as an adapted stochastic process aud provide all necessary proofs in detail.