Unexpected absorption in the real atmosphere in the window from 840 to 890 nm has been clearly observed through measurements of direct solar spectral irradiance under clear, cloud-free skies. This absorption is not predicted by the known theoretical models. The cause of this apparent absorption may be due to the presence of high thin nonvisible cirrus clouds. A quantitative evaluation of this absorption and an improvement of oxygen absorption coefficients has been carried out after a comparison of more than seventy experimental spectra. Moreover, it is necessary to take into account the different behavior of modeled and experimental data at low and high air masses.