The aim of this study was to test the hypothesis that the maximal instantaneous muscular power of humans ( $$ \dot{w} $$ p) is affected by the negative work performed immediately before the jump (w n), possibly due to the recoil of elastic strain energy stored in previously stretched series-elastic elements of the muscle–tendon complex. Twenty-seven Bantu subjects (age 25.1 ± 4.3 years, body mass 67.5 ± 7.8 kg) were investigated. The $$ \dot{w} $$ p, the average power ( $$ \dot{w} $$ a) and w n were determined during maximal vertical jumps off both feet on a force platform. Three jumping conditions were studied: squat jumps (SQ), countermovement jumps (CM), and jumps preceded by a free fall (FF) from a height of 0.3 m above the platform surface. The w n was higher in CM than in SQ and in FF than in CM and SQ. The $$ \dot{w} $$ p was 3.51 ± 0.54 kW in SQ and did not vary in CM and FF. The $$ \dot{w} $$ a increased with increasing w n (1.70 ± 0.30; 1.85 ± 0.34; 1.99 ± 0.31 kW in SQ, CM and FF, respectively, p < 0.05). The greater was the w n, the higher was the force at the start of the positive push phase, and thus the maximal force attained during the push phase. In conclusion, $$ \dot{w} $$ p was independent of w n, whereas $$ \dot{w} $$ a was affected, because a greater force was developed over a shorter time during the push. The independence of $$ \dot{w} $$ p of w n leads to refutation of the tested hypothesis.