In this paper, non-parallel and parallel taxicab bisectors are defined. Properties of these taxicab bisectors are examined. In Chapter 1, the different ways that taxicab bisectors can intersect each other are discussed. In Chapter 2, conditions for taxicab bisectors to be parallel are presented. Special emphasis is placed on showing that taxicab geometry is non-euclidean. Finally in Chapter 3. some ideas for further research are suggested.