  Let $P(M)$ be the matroid base polytope of a matroid $M$. A {\em matroid base
polytope decomposition} of $P(M)$ is a decomposition of the form $P(M) =
\bigcup\limits_{i=1}^t P(M_{i})$ where each $P(M_i)$ is also a matroid base
polytope for some matroid $M_i$, and for each $1\le i \neq j\le t$, the
intersection $P(M_{i}) \cap P(M_{j})$ is a face of both $P(M_i)$ and $P(M_j)$.
In this paper, we investigate {\em hyperplane splits}, that is, polytope
decompositions when $t=2$. We give sufficient conditions for $M$ so $P(M)$ has
a hyperplane split and characterize when $P(M_1 \oplus M_2)$ has a hyperplane
split where $M_1 \oplus M_2$ denote the {\em direct sum} of matroids $M_1$ and
$M_2$. We also prove that $P(M)$ has not a hyperplane split if $M$ is binary.
Finally, we show that $P(M)$ has not a decomposition if its 1-skeleton is the
{\em hypercube}.
