  We investigate a model closely related to both the original Sachdev-Ye-Kitaev
(SYK) model and the $\mathcal{N}=1$ supersymmetric SYK model. It consists of
$N$ real Majorana fermions and $M$ auxiliary bosons with Yukawa interactions.
We consider the large $N$ and $M$ limit and keep the ratio $M/N$ fixed. The
model has two branches characterized by the conformal dimensions of fields,
which we compute as a function of the ratio $M/N$. One of the branches contains
the supersymmetric saddle for $M=N$. Furthermore, we determine the Lyapunov
exponent of the model and find maximal chaos independent of $M/N$.
