The calculation of the near-surface turbulent fluxes of energy and momentum in climate and weather prediction models requires transfer coefficients. Currently used parametrizations of these coefficients are based on stability functions derived from measurements over land and not over sea ice. However, recently, a non-iterative parametrization has been proposed by Gryanik and Lüpkes (2018), which can be applied to climate and weather prediction models as well but uses stability functions of Grachev et al. (2007). These functions had been obtained from measurements during the Surface Heat Budget over the Arctic Ocean campaign (SHEBA) and thus from measurements over sea ice. A drawback of the scheme of Gryanik and Lüpkes (2018) is that there is still some complexity due to the complexity of the SHEBA based functions. Thus new stability functions are proposed for the stable boundary layer, which are also based on the SHEBA measurements but avoid the complexity. It is shown that the new functions are superior to the former ones with respect to the representation of the measured relationship between the Obukhov length and the bulk Richardson number. Moreover, the resulting transfer coefficients agree slightly better with the SHEBA observations in the very stable range. Nevertheless, the functions fulfill the same criteria of applicability as the earlier functions and contain furthermore as an extension a dependence on the neutral Prandtl number. Applying the new functions, an efficient non-iterative parametrization of the near-surface turbulent fluxes of momentum and heat is developed where transfer coefficients result as a function of the bulk Richardson number (Rib) and roughness parameters. The new transfer coefficients, which are recommended for weather and climate models, agree well with the SHEBA data in a large range of stability (0< Rib<0.5) and with those based on the Dyer-Businger functions in the range Rib <0.08.