We investigated the stability of the supercooled liquid in Zr-based glassy alloys by examination of their transformation behavior. The primary phase is an fcc Zr₂Ni phase in a Zr₆₅Al_7.5Ni₁₀Cu_17.5 glassy alloy with high glass-forming ability (GFA). By substitution of Ag, Pd, Au or Pt for only 1 at%Cu, an icosahedral quasicrystalline phase (I-phase) precipitates with the fcc Zr₂Ni phase. The primary phase changes to the single I-phase at higher noble metal contents. It is further found that the I-phase precipitates by a small amount of substitution for Cu with other elements as well as the noble metals, which have a weak or positive chemical affinity with one of the constitutional elements in the Zr–Al–Ni–Cu glassy alloy. Thus, the slight deviation from the three component rules for high GFA is effective for the I-phase formation. The I-phase is also formed as a primary phase in the Zr_65+yAl_7.5Ni₁₀Cu_17.5−y (y=1–7) glassy alloys. A slight change in the composition has the similar effect as the addition of element such as noble metals and so on. An icosahedron is contained as a structure unit in the fcc Zr₂Ni and I-phases and hence the glassy structure is correlated with the local icosahedral atomic configuration. The high-resolution transmission electron microscopy image of the Zr₇₀Al_7.5Ni₁₀Cu_12.5 glassy alloy reveals a possibility of the existence of the icosahedral ordered regions. It is therefore, concluded that the icosahedral short- or medium-range order exists in the supercooled liquid as well as in the glassy phase and it stabilizes the supercooled liquid state in the Zr-based alloys. An I-phase also precipitates as a primary phase by substituting Pd, Au or Pt for only 1 at%Cu in the Zr₇₀Cu₃₀ glassy alloy. From these results, the appearance of the supercooled liquid region is attributed to the existence of the icosahedral atomic configuration consisting of Zr and Cu.