We studied the properties and proper motions of Ellerman bombs (EBs) around a sunspot in a mature active region using high-resolution off-band Hα filtergrams together with nearly simultaneous magnetograms. Sixty-four percent of the EBs (class I) did not correspond accurately to enhanced magnetic field elements while the rest corresponded well to such elements (class II), which all were moving magnetic features (MMFs). We studied the lifetimes, shapes and dimensions, contrasts and time profiles of the EBs. These properties were essentially the same for both classes, in agreement with previous authors. Class I EBs did not move but class II EBs tracked the MMFs well, with horizontal proper motions up to a maximum of 1.1 km s−1 and their velocity pattern was similar to the velocity pattern of the MMFs.