We present moderate-resolution (lambda/Delta lambda = 1300-4800) K-band spe
ctra of more than 110 M giants in Galactic bulge fields interior to -4 degr
ees (560 pc) and as close as within 0.degrees 2 (28 pc) of the Galactic cen
ter. From the equivalent widths of three features in these spectra, EW(Na),
EW(Ca), and EW(CO) we calculate metallicities for the stars with a new cal
ibration derived by Stephens et al. from globular clusters. The mean metall
icity for each field is in good agreement with the recent results from Frog
el et al. based on the slope of the giant branch method. We find no evidenc
e for a metallicity gradient along the minor or major axes of the inner bul
ge (R < 560 pc). The lack of a metallicity gradient in the inner bulge is n
ot predicted by a theoretical model developed by Molla et al. for a bulge f
ormed by dissipative collapse. A metallicity gradient along the minor axis
found by Frogel et al. only arises when fields located at larger galactic r
adius are included. However, these more distant fields are located outside
of the infrared bulge defined by the COBE/DIRBE observations. We compute th
e metallicity distribution for the inner bulge and find a mean value of -0.
21 dex with a dispersion of +/-0.30 dex, close to the values found in 1996
by Sadler ct al. for Baade's window. Unlike the absence of a gradient, thes
e values are close to theoretical predictions for a bulge formed by dissipa
tive collapse.