In　this　paper,　we　develop　the　matrix-analytic　method　to　discuss　an　interesting　but　challenging　bilateral　stochastic　matching　problem:　A　matched　queue　with　matching　batch　pair　(m,n)　and　two　types　of　impatient　customers,　where　the　two　types　of　customers　arrive　according　to　two　independent　Poisson　processes.　Once　m　A-customers　and　n　B-customers　are　matched　as　a　group,　the　m+n　customers　immediately　leave　the　system.　We　show　that　this　matched　queue　can　be　expressed　as　a　novel　bidirectional　level-dependent　quasi-birth-and-death　(QBD)　process　whose　analysis　has　its　own　interests,　and　specifically,　computing　the　maximal　non-positive　inverse　matrices　of　bidirectional　infinite　sizes　by　using　the　RG-factorizations.　Based　on　this,　we　can　provide　an　effective　matrix-analytic　method　to　deal　with　this　matched　queue,　including　the　system　stability,　the　average　stationary　queue　lengths,　the　average　sojourn　times,　and　the　departure　process.　We　believe　that　the　methodology　and　results　developed　in　this　paper　can　be　applicable　to　studying　more　general　matched　queueing　systems,　which　are　widely　encountered　in　many　practical　areas.　©　2024　Elsevier　B.V.