  Under consideration of coordinate conditions, we get the
Schwarzschild-Beltrami-de Sitter (S-BdS) metric solution of the Einstein field
equations with a cosmological constant $\Lambda$. A brief review to the de
Sitter invariant special relativity (dS-SR), and de Sitter general relativity
(dS-GR, or GR with a $\Lambda$) is presented. The Beltrami metric $B_{\mu\nu}$
provides inertial reference frame for the dS-spacetime. By examining the
Schwarzschild-de Sitter (S-dS) metric $g_{\mu\nu}^{(M)}$ existed in literatures
since 1918, we find that the existed S-dS metric $g_{\mu\nu}^{(M)}$ describes
some mixing effects of gravity and inertial-force, instead of a pure gravity
effect arisen from "solar mass" $M$ in dS-GR. In this paper, we solve the
vacuum Einstein equation of dS-GR, with the requirement of gravity-free metric
$g_{\mu\nu}^{(M)}|_{M\rightarrow 0}=B_{\mu\nu}$. In this way we find S-BdS
solution of dS-GR, written in inertial Beltrami coordinates. This is a new form
of S-dS metric. Its physical meaning and possible applications are discussed.
