  Grover's search algorithm searches a database of $N$ unsorted items in
$O(\sqrt{N/M})$ steps where $M$ represents the number of solutions to the
search problem. This paper proposes a scheme for searching a database of $N$
unsorted items in $O(logN)$ steps, provided the value of $M$ is known. It is
also shown that when $M$ is unknown but if we can estimate an upper bound of
possible values of $M$, then an improvement in the time complexity of
conventional Grover's algorithm is possible. In that case, the present scheme
reduces the time complexity to $O(MlogN)$.
