A scanning probe microscope capable of preventing contact between the probe and a sample and a method of operating this microscope. The scanning probe microscope measures the topography of a surface of the sample by scanning the probe relative to the surface of the sample. A scanning reference position in the heightwise direction is updated in response to a maximum value of the height of the surface of the sample on the scan lines scanned so far. A limit value is set for motion of the probe in the heightwise direction relative to the scanning reference position. After the update, the next scan line is scanned. In this way, scanning is carried out along the successive scan lines.