  We study the origins of the inaccuracies of Schwinger's nonet mass, and the
Sakurai mass-mixing angle, formulae for the pseudoscalar meson nonet, and
suggest new versions of them, modified by the inclusion of the pseudoscalar
decay constants. We use these new formulae to determine the pseudoscalar decay
constants and mixing angle. The results obtained, $f_8/f_\pi = 1.185\pm 0.040,$
$f_9/f_\pi =1.095\pm 0.020,$ $f_\eta /f_\pi = 1.085\pm 0.025,$ $f_{\eta
^{'}}/f_\pi =1.195\pm 0.035,$ $\theta = (-21.4\pm 1.0)^o,$ are in excellent
agreement with experiment.
