Searches for double beta decay of $^{134}$Xe were performed with EXO-200, a single-phase liquid xenon detector designed to search for neutrinoless double beta decay of $^{136}$Xe. Using an exposure of $29.6text{ kg}!cdot!text{yr}$, the lower limits of $text{T}_{1/2}^{2 ubeta!beta}>8.7cdot10^{20}text{ yr}$ and $text{T}_{1/2}^{0 ubeta!beta}>1.1cdot10^{23}text{ yr}$ at 90% confidence level were derived, with corresponding half-life sensitivities of $1.2cdot10^{21}text{ yr}$ and $1.9cdot10^{23}text{ yr}$. These limits exceed those in the literature for $^{134}$Xe, improving by factors of nearly $10^{5}$ and 2 for the two antineutrino and neutrinoless modes, respectively.
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