We have been developing monolithic active pixel sensors with $0.2~\mu{\hbox {m}}$ Silicon-On-Insulator (SOI) CMOS technology, called SOIPIX, for high-speed wide-band X-ray imaging spectroscopy on future astronomical satellites. In this work, we investigate a revised chip (XRPIX1b) for soft X-rays used in frontside illumination. The ${\hbox {Al~ K}}\alpha$ line at 1.5 keV is successfully detected and energy resolution of 188 eV (FWHM) is achieved from a single pixel at this energy. The responsivity is improved to $6~\mu {\hbox {V/electron}}$ and the readout noise is 18 electrons rms. Data from $3 \times 3~{\hbox {pixels}}$ irradiated with 6.4 keV $({\hbox {Fe~K}} \alpha)$ X-rays demonstrates that the circuitry crosstalk between adjacent pixels is less than 0.5%.