Dissipative solitons, which result from the intricate balance between dispersion and nonlinearity as well as gain and loss, are of the fundamental scientific interest and numerous important applications. Here, we report a fiber laser that generates bisoliton - two consecutive dissipative solitons that preserve a fixed separation between them. Deviations from this separation result in its restoration. It is also found that these bisolitons have multiple discrete equilibrium distances with the quantized separations, as is confirmed by the theoretical analysis and the experimental observations. The main feature of our laser is the anomalous dispersion that is increased by an order of magnitude in comparison to previous studies. Then the spectral filtering effect plays a significant role in pulse-shaping. The proposed laser has the potential applications in optical communications and high-resolution optics for coding and transmission of information in higher-level modulation formats.