The effect of heat treating temperature and ${\alpha}$ phase In the ${\beta}$ phase matrix were investigated for ${\beta}-CuZnAl$ shape memory alloys by tension test, fatigue test, and shape memory effect test. After heat treatment at $677^{\circ}C$, $750^{\circ}C$, $800^{\circ}C$ and $850^{\circ}C$ for 10 min. respectively, static fracture stress(${\sigma}_f$), fatigue fracture stress(${\tau}_{max}$) at $10^6$ cycle, and elongation(${\epsilon}_f$) was $24.2kg/mm^2$, $17.21kg/mm^2$ and 11.8%, respectively. As heat treating temperature decreased, fracture surfaces of the specimens were changed from the intergranular to the transgranular fracture mode. Especially, the a phase precipitated in the ${\beta}$ phase matrix had an effect on crack propagation and the fracture surface was characterized by dimple-like pattern when crack propagated in transgranular cracking mode. Precipitation of the ${\alpha}$ phase in the ${\beta}$ phase matrix lowered the transformation temperature by $10^{\circ}C$, and about 2.5 vol.% ${\alpha}$ phase did not affect the shape memory effect examined by the bending test.