Standard magnetic force microscopy (MFM) is considered as a powerful tool used for magnetic field imaging at nanoscale. The method consists of two passes realized by the magnetic tip. Within the first one, the topography pass, the magnetic tip directly touches the magnetic sample. Such contact perturbs the magnetization of the sample explored. To avoid the sample touching the magnetic tip, we present a new approach to magnetic field scanning by segregating the topological and magnetic scans with two different tips located on a cut cantilever. The approach minimizes the disturbance of sample magnetization, which could be a major problem in conventional MFM images of soft magnetic samples. By cutting the cantilever in half using the focused ion beam technique, we create one sensor with two different tips--one tip is magnetized, and the other one is left non-magnetized. The non-magnetized tip is used for topography and the magnetized one for the magnetic field imaging. The method developed we call dual-tip magnetic force microscopy (DT-MFM). We describe in detail the dual-tip fabrication process. In the experiments, we show that the DT-MFM method reduces significantly the perturbations of the magnetic tip as compared to the standard MFM method. The present technique can be used to investigate microscopic magnetic domain structures in a variety of magnetic samples and is relevant in a wide range of applications, e.g., data storage and biomedicine.