The phenomenon of electronic orbital angular momentum L uncoupled from its internuclear axis has been observed in the sodium dimer using high-resolution cw optical-optical double-resonance spectroscopy. When L uncoupling occurs, the degeneracy of Lambda doubling is removed. In our experiment, the intermediate B (1)Pi(u) state of Na(2) is excited from the thermally populated ground X (1)Sigma(g) (+) state by a single-line Ar(+) laser. Then, a single-mode dye laser is used to probe the Rydberg states from the intermediate state. The signals are detected by monitoring the UV fluorescence from the triplet gerade states back to the a (3)Sigma(u) (+) state via collision energy transfer. Under our experimental resolution, the splitting of Lambda doubling in the 5 (1)Delta(g) state of Na(2) can be measured. A total of 136 rovibronic levels with ef parities have been assigned to the 5 (1)Delta(g) state. The Lambda-splitting constants deduced from these data are q(0)=0.376(90)x10(-4) cm(-1), q(v)=0.114(6)x10(-4) cm(-1), and mu=0.76(33)x10(-8) cm(-1). In general, the Lambda splitting of the Delta states is considerably smaller than that of the Pi states. However, the first-order splitting constants q(0) and q(v) reported here are larger than those in the B (1)Pi(u) state. This is due to the L uncoupling of the Rydberg states.