A search for exclusive decays of Bd⁰ and Bs⁰ mesons has been performed in the channels Bd⁰ → Jη, Bs⁰ → Jη, Bd⁰ → Jπ⁰ and Bs⁰ → Jπ⁰. The data sample consisted of more than three and half million hadrozic Z decays collected by the L3 experiment at LEP from 1991 through 1995. No candidate events have been observed for any of the modes thus determining upper limits at 90% confidence level: 3.2 × 10⁻⁴ on Br(Bd⁰ → Jπ⁰) and the first experimental limits: Br(Bd⁰ → Jη) < 1.2 × 10⁻³, Br(Bs⁰ → Jη) < 3.8 × 10⁻³, Br(Bs⁰ → Jπ⁰) < 1.2 × 10⁻³.