New monthly estimates of the Earth's gravity field determined solely from GRACE inter-satellite range-rate measurements using an improved method of accelerometer calibration and the use of a baseline state parameterization are presented in this paper. Our methodology exploits the inherent power of the inter-satellite range-rate data at the expense of the GPS data, which are used solely for establishing an accurate orbital reference and for calibrating accelerometers. Resulting gravity solutions show significantly less error than previously published GRACE solutions, especially for spherical harmonic terms of degree 2 and terms of order 15,16.