  We prove that, for sufficiently large $n$, every graph of order $n$ with
minimum degree at least $0.852n$ has a fractional edge-decomposition into
triangles. We do this by refining a method used by Dross to establish a bound
of $0.9n$. By a result of Barber, K\"{u}hn, Lo and Osthus, our result implies
that, for each $\epsilon >0$, every graph of sufficiently large order $n$ with
minimum degree at least $(0.852+\epsilon)n$ has a triangle decomposition if and
only if it has all even degrees and number of edges a multiple of three.
