During the search for new functional alloys, Zr—Nb system is investigated. The investigations concerning the presence of the martensitic transformation (MT) and shape-memory effect are performed; composition features are explored by microstructural and X-ray analysis techniques. As found, the MT in the Zr—Nb system takes place in a wider range of niobium concentrations than it was previously estimated. The presence of the shape-memory effect in Zr$_{93}$Nb$_{7}$ and Zr$_{86}$Nb$_{14}$ alloys is firstly observed. Characteristic MT temperatures decrease with increasing niobium concentration. Due to both the bioinertness and the MT temperatures close to the human body temperature, Zr$_{86}$Nb$_{14}$ alloy can be promising for further in-depth study in order to use it in the healthcare industry.