A unidirectional anisotropy appears in field cooled samples of dilute magnetic alloys at temperatures well below the cusp temperature of the zero field cooled magnetization curve. Magnetization measurements on a Cu(13.5 at% Mn) sample show that this anisotropy is essentially temperature independent and acts on a temperature dependent excess magnetization, ΔM. The anisotropy can be partially or fully transferred from being locked to the direction of the cooling field at lower fields to becoming locked to the direction of ΔM at larger fields, thus instead appearing as a uniaxial anisotropy. This introduces a deceiving division of the anisotropy into a superposition of a unidirectional and a uniaxial part. This two faced nature of the anisotropy has been empirically scrutinized and concluded to originate from one and the same exchange mechanism: the Dzyaloshinsky-Moriya interaction.