The magnetostriction versus field (${lambda}-H$) curves for the melt-spun ribbons of $Dy_{x}{(Fe_{1-y}B_{y})}_{1-x}$ (x=0.2, 0.25, 0.3; y=0, 0.05, 0.1, 0.15, 0.2) alloys are measured systematically at various wheel speeds ranging from 10 to 50 m/sec. The ${lambda}-H$ curves in most cases vary sensitively with the wheel speed and, in the wheel speed range where no amorphous phase is formed, the magnetic softness improves rather continuously with the wheel speed. This result is considered to be due to the reduced grain size with increasing wheel speed, which was confirmed by X-ray diffraction and transmission electron microscopy. In particular, homogeneous and ultrafine grains with size of about 10 nm are formed even in the as-spun state when the $Dy_{0.3}{(Fe_{1-y}B_{y})}_{0.7}$ alloys are quenched at the wheel speed of 30 m/sec (for the alloy with y=0.2) or 40 m/sec (for the alloys with $y{leq}0.15$) and the ribbons having the nanocrystalline grain structure exhibit good magnetostrictive characteristics.