In correlated electron materials, superconductivity and magnetic order are often occurring in close proximity - subtle changes of doping, pressure or chemical composition can turn a material magnetically ordered or superconducting. Understanding the relation between the two is believed to be key for understanding the physics of unconventional superconductivity in correlated electron materials. Among the parent compounds of the iron based superconductors, the magnetic structure of FeTe is unique -- not only is it rotated by 45° with respect to the magnetic structure found in the iron-pnictide materials, it is also not connected to a nesting vector between different sheets of the Fermi surface. At increased excess iron concentrations y, the magnetic structure becomes incommensurate. Here, we report scanning tunnelling microscopy of a unidirectional modulation in FeTe. Our data confirm that in the monoclinic phase, the modulation is truly unidirectional, separated in different domains, whereas in the orthorhombic phase at higher excess iron concentration y>0.12, a transition to a phase with coexistence in both directions within a single domain is observed.