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Generally the Brans-Dicke theory reduces to General Relativity in the limit$\omega\rightarrow\infty$ if the scalar field goes as $\phi\propto1/\omega$.However, it is also known that there are examples with$\phi\propto1/\sqrt{\omega}$ that does not tend to GR. We discuss another case:a homogeneous and isotropic universe filled with stiff matter. The power oftime dependence of these solutions do not depend on $\omega$, and there is noGeneral Relativity limit even though we have $\phi\propto1/\omega$. Aperturbative analysis of this exotic case is carried out.

Stiff Matter Solution in Brans-Dicke Theory and The General Relativity Limit