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Consider ${𝒯}_n\left(F\right)$—the ring of all $n\times n$ upper triangular matrices defined over some field $F$. A map $\phi$ is called a zero product preserver on ${𝒯}_n\left(F\right)$ in both directions if for all $x,y\in {𝒯}_n\left(F\right)$ the condition $xy=0$ is satisfied if and only if $\phi \left(x\right)\phi \left(y\right)=0$. In the present paper such maps are investigated. The full description of bijective zero product preservers is given. Namely, on the set of the matrices that are invertible, the map $\phi$ may act in any bijective way, whereas for the zero divisors and zero matrix one can write $\phi$ as a composition...