A　graph　is　said　to　be　ISK4-free　if　it　does　not　contain　any　subdivision　of　K4　as　an　induced　subgraph.　Leveque,　Maffray　and　Trotignon　conjectured　that　every　ISK4-free　graph　is　4-colorable.　In　this　paper,　we　show　that　this　conjecture　is　true　for　the　class　of　{ISK4,　diamond,　bowtie}-free　graphs,　where　a　diamond　is　the　graph　obtained　from　K4　by　removing　one　edge　and　a　bowtie　is　the　graph　consisting　of　two　triangles　with　one　vertex　identified.