  We obtain the most general ensemble of qubits, for which it is possible to
design a universal Hadamard gate. These states when geometrically represented
on the Bloch sphere, give a new trajectory. We further consider some Hadamard
`type' of operations and find ensembles of states for which such
transformations hold. Unequal superposition of a qubit and its orthogonal
complement is also investigated.
