high-z galaxies due to their faint continuum. Furthermore, the number of objects which can be observed at a time is limited depending on slit configuration. Therefore, it is impractical to accurately measure the continuum flux from spectroscopic data for all the $\sim$ 1800 targets in our sample. Instead, we apply the simple power-law fitting to the broad-band photometry with the following functional form, $$M(\lambda_{x}) = -2.5 (\beta + 2) \log \lambda_{x} + Const
\label{eq1}$$

where $\lambda_{x}$ is the effective wavelength of $x$th broad-band filter, $M$($\lambda_{x}$) is the measured magnitude of $x$th broad-band filter, and [*Const*]{} is a constant value. This method is suitable since the bias in the $\beta$ estimation is small ([@Fink12]; [@Rog13]). For the fitting, we conduct the least square fitting to the *i’*, *z’*, updated-*z’*, and *J* band filters which cover the rest-frame wavelength from $\sim$ 1500Å to $\sim$ 2500Å for the objects at *z* $=$ 3.5–4.5. In our analysis, an uncertainty of the $\beta$ value represents the uncertainty of the least square fitting when taking account of the photometric error of the broad-band filters.

Although using the larger number of the photometry data points results in more accurate determination of the UV slope $\beta$ value, we 