Let P and Q be two idempotents on a Hilbert space. In 2005, J. Giol in [Segments of bounded linear idempotents on a Hilbert space, J. Funct. Anal. 229(2005) 405-423] had established that, if P + Q - I is invertible, then P and Q are homotopic with s(P,Q) < 2. In this paper, we have given a necessary and sufficient condition that s(P,Q) < 2, where s(P, Q) denotes the minimal number of segments required to connect not only from P to Q, but also from Q to P in the set of idempotents.