In order to gain a better understanding of the origin of decoherence in
superconducting flux qubits, we have measured the magnetic field dependence of
the characteristic energy relaxation time (T1) and echo phase relaxation
time (T2echo) near the optimal operating point of a flux qubit. We
have measured T2echo by means of the phase cycling method. At the
optimal point, we found the relation T2echo≈2T1. This means
that the echo decay time is {\it limited by the energy relaxation} (T1
process). Moving away from the optimal point, we observe a {\it linear}
increase of the phase relaxation rate (1/T2echo) with the applied
external magnetic flux. This behavior can be well explained by the influence of
magnetic flux noise with a 1/f spectrum on the qubit