We propose and numerically verify a scheme of phase-sensitive amplifier (PSA) using four-wave mixing (FWM) in cascaded highly nonlinear fibres (HNLFs), without requiring initial phase-locking between signal and pump. The first HNLF is used to generate two phase-conjugate waves, which act as two pumps for FWM process in second HNLF. We feed the two pumps from opposite ends of second HNLF and a signal co-propagating with one of the pumps. We keep the signal frequency in the middle of two pump frequencies to obtain phase-conjugate wave at the same frequency as the signal by FWM process in second HNLF. Signal and phase-conjugate wave appear at opposite ends of the second HNLF and combined to obtain PSA. The frequency-shift-free operation of phase conjugation helps in preserving the frequency of input signal during phase-sensitive amplification. We derive the expression for PSA signal output and PSA gain and show analytically that PSA gain depends upon signal phase only, as the two pumps are phase conjugate to each other. Thus, eliminating the need of phase locking between signal and pump waves. We show that PSA provides high gain for in-phase component and almost cancellation for quadrature-phase component of signal. We show the broadband nature of PSA due to minimum effect of group velocity and group velocity dispersion owing to counter-propagating nature of signal and conjugate waves. We study the performance of PSA under the effects of pump-signal detuning, amplifier length and input signal phase. Simulation results show that PSA output is forced to attain 0 or π phase regardless of large variation of phase in the input signal. Nonlinear phase noise reduction of 100 Gbps DPSK signal transmitted over 1000-km standard single-mode fibre confirms phase regeneration by PSA.