In this paper, we propose an improved model-independent method to constrain the cosmic curvature by combining the most recent Hubble parameter H(z) and supernovae Ia (SNe Ia) data. Based on the H(z) data, we first use the model-independent smoothing technique, Gaussian processes, to construct a distance modulus mu(H)(z) which is susceptible to the cosmic curvature parameter Omega(k). In contrary to previous studies, the light-curve-fitting parameters, which account for the distance estimation of SN (mu(SN)( z)), are set free to investigate whether Omega(k) has a dependence on them. By comparing mu(H)(z) to mu(SN)(z), we put limits on Omega(k). Our results confirm that Omega(k) is independent of the SN light-curve parameters. Moreover, we show that the measured Omega(k) is in good agreement with zero cosmic curvature, implying that there is no significant deviation from a flat universe at the current observational data level. We also test the influence of different H(z) samples and different Hubble constant H-0 values, finding that different H( z) samples do not have a significant impact on the constraints. However, different H-0 priors can affect the constraints of Ok to some degree. The prior of H-0 = 73.24 +/- 1.74 km s(-1) Mpc(-1) gives a value of Omega(k), a little bit above the 1 sigma confidence level away from 0, but H-0 = 69.6 +/-. 0.7 km s(-1) Mpc(-1) gives it below 1 sigma.