## 1 Introduction  
The prosthetic gait is characterized by a relatively low walking speed [1], high asymmetry [2], and high metabolic cost [3]. Kinematically, concentric contraction of the hip flexors is needed to compensate for the loss of ankle plantar flexion for sufficient foot clearance [4]. During the single support phase, the ankle joint on the non-amputated side excessively plantar flexes to assist toe clearance [5]. Changes also occur in the hip, knee, and ankle joints for both the amputated and non-amputated limbs. These were described as a compensatory mechanism, which is an explanation for the adaptation control strategy for amputees [5; 6]. Motion capture systems (MOCAP) accompanied with force platforms are commonly used to investigate the locomotion of transfemoral amputees and compensatory motion. Reduced stance time and impulse was found in the prosthetic limb during level walking [2], whilst transfemoral amputees demonstrated greater prosthetic knee joint extension and moment during stair ascent [7; 8]. There was no significant difference in intact limb loading during slope descend compared to the able-bodied control, despite the fact that transfemoral amputees walked slower and with smaller steps [9]. [PERSON] et al. [10] aimed to identify the compensatory gait in 60 amputees and found that they lacked prosthetic knee flexion and intact side hip extension in early stance and late stance respectively, whereas propulsive force on the prosthetic limb was insufficient in late stance. Besides, evaluations of prosthetic designs were also conducted using MOCAP. For example, customized prosthetic socket [11], microprocessor-controlled prosthetic knee joints [6], and bionic prosthetic foot [12], etc. While researchers have attempted to quantify the deviations in the prosthetic gait using kinematic or kinetic parameters [13], they overlooked the effects of the coupling and interactions between joints. Human locomotion is characterized by multiple-degrees of freedom movement, which requires different body segments and joints to cooperate with each other for achieving a precise foot trajectory [14; 15; 16]. For transfemoral amputees, the objective is to reduce the redundancy in the degrees of freedom for movement to achieve a stable, smooth, and accurate gait. In studies on inter-joint coordination, the interactions or coupling effects were considered by evaluating the multiple degrees of freedom in the movement. These included the interactions between two joints and contemplated the timing and sequencing of the motor control. In other studies on inter-joint coordination, the effects of obstacle-crossing [17], age [18], walking speed [19], muscle fatigue [20], treadmill walking [21], and pathologies such as ankle sprain [22] and knee osteoarthritis [23]. Relevant understanding of the inter-joint coordination for transfemoral amputees could help design linkages that synergize prosthetic joints, feet, or other components, and facilitate safe and energy-saving gait for them. Parameters commonly used to evaluate inter-joint coordination include the continuous relative phase (CRP) [24] and the decomposition index (DI) [25; 26]. The CRP is a continuous measurement of joint interaction derived from the differences in the phase angle between two joints, while the phase angle depends on both the joint angle and the angular velocity during walking [23; 27; 28]. In decomposition movement, one of the paired joints is rotated while the other joint is kept still. This strategy is used to reduce redundancy [29]. The DI was defined as the duration ratio of the decomposition movement [25; 26]. The objective of this study was to investigate the inter-joint coordination (via the CRP and DI) of the amputated and non-amputated limbs of transfemoral amputees during level walking and to compare it with that for able-bodied individuals.