  Paul Erd\H{o}s and L\'{a}szl\'{o} Lov\'{a}sz established by means of an
example that there exists a maximal intersecting family of $k-$sets with
approximately $(e-1)k!$ blocks. L\'{a}szl\'{o} Lov\'{a}sz conjectured that
their example is best known example which has the maximum number of blocks.
Later it was disproved. But the quest for such examples remain valid till this
date. In this short note, by computing transversal size of a certain series of
uniform intersecting families constructed over the cycle graph, we provide an
example which has more than $(\frac{k}{2})^{k-1}$ (approximately) blocks.
